Search

• A novel beam-spring 2-DOF magnetically coupled bistable energy harvester is proposed. • The operating bandwidth is improved by approximately 60 % compared with a CBEH. • The subharmonic responses are characterized by the coexistence of two coupling modes. • Reasonable spring stiffness design is helpful to further enhance the bandwidth. • The excitation threshold peak effect of the 2-DOF coupled system is studied. Introducing the magnetic coupling effect with multiple degrees of freedom to a conventional bistable energy harvester is helpful to further enhance its operating bandwidth. However, it is not straightforward to design due to its extremely complicated dynamic characteristics, meanwhile, some underlying mechanisms also need to be explored ulteriorly. This paper proposes a novel beam-spring two-degree-of-freedom magnetically coupled bistable energy harvester, combining the advantages of multistable and multimodal harvesters. Based on the theoretical model validated by experiments, the complex nonlinear dynamic behaviors of the system are investigated in detail, as well as the effects of key parameters on power generation capacity. It is found that the working bandwidth is improved by more than 60 % because of the additional contribution from the 2nd resonance region. And there are abundant interwell ultraharmonic and subharmonic responses characterized by the coexistence of out-of-phase and in-phase coupling modes. Under appropriate spring stiffness or certain initial conditions, the snap-through motion can be successfully triggered to enter a high-energy orbit. The parameter study shows that the magnet distance and spring stiffness significantly affect the effective bandwidth. Furthermore, the excitation threshold peak effect that hinders the connection of the two resonant frequency bands is also observed. Fortunately, it can be eliminated by the reasonable design of the 1st and 2nd natural frequencies to achieve a consecutive and broad effective bandwidth. This research provides a theoretical case for designing and developing wide-band and low-threshold bistable energy harvester. [Display omitted] [ABSTRACT FROM AUTHOR]

• Displacement feedback is used to control friction-induced stick-slip oscillation. • The linear stability analysis of the controlled system is carried out. • Optimization of control parameters is performed by pole-crossover design. • The effect time delay on the control is investigated. • Averaging method is used to study the dynamics of nonlinear system. The present work utilizes a displacement feedback control strategy to mitigate the friction driven stick-slip vibration of a mechanical system with single degree of freedom. The stick-slip vibration is primarily caused by the decrease in friction force due to the changes in velocity of the moving surface. This phenomenon, also known as Stribeck effect, can have a negative impact on the system's performance. A mass on a moving belt is considered as the primary system for stick-slip vibration. The dynamics of stick slip oscillation is represented by the polynomial model. Prior to being sent to the system, the displacement signal of the mass undergoes processing via a filter to effectively control the friction induced instability. Eigenvalue analysis of the linearized controlled system is carried out to obtain the boundary line at which the static equilibrium switches its stability. To conduct the nonlinear analysis, the method of averaging is utilized and the resulting outcomes are then verified through simulation results. The bifurcation analysis shows that the controller has the capability to eliminate undesired oscillations and stabilize the system. In order to optimize the filter parameters, the pole crossover method is utilized. The amplitude of the vibration is seen to be reduced significantly by applying the proposed control. Finally, theoretical study of the nonlinear behavior of the controlled system is carried out while taking into account the existence of time delay. [ABSTRACT FROM AUTHOR]

In earthquake-prone areas, seismic isolation systems are designed to preserve structural safety and prevent occupants' injury and properties' damage. However, seismically isolated structures can be subject to large displacements relative to the ground under earthquakes, which lead to define two problems, the first problem concerns to excessive displacements, whereas the second problem relates to excessive accelerations that occur when the displacements are limited by an obstacle with high relative stiffness. An arrangement that favors the solution of these problems is an appropriate interposition between the isolated structure and the obstacle of the shock absorbers or bumpers. The aim of this paper is to investigate, via numerical parametric analyses, the possibility to exploit the occurrence of impact in a two-sided vibro-impact isolated single-degree-of-freedom (SDOF) system under harmonic base excitation with beneficial effects. Through the analysis of the response scenarios which can occur varying the obstacles' parameters, that is the width of the gap and the mechanical (stiffness and damping) properties, the target is to reduce both the maximum value of the displacement and of the acceleration of the mass, compared to the free flight condition, without possibly reducing the vibration isolation frequency range. This research path leads to the definition of vibro-impacting control systems and to the free and constrained single and multi-objective optimal design of the control system consisting of the integrated assembly of the isolation system, bumpers and gaps. The main results obtained consist in having (i) found a unique optimality condition, (ii) calculated the dissipated energy and given an energetic interpretation to the optimality condition (iii) built maps, that allow to advance behavior predictions, provide indications on the design and allow to make evaluations of the performance of the vibro-impacting system as a function of the stiffness and damping parameters and of the width of the gap. The stiffness ratio and the damping ratio, which define the mechanical properties of the bumpers, are such that the dimensionless relaxation time is about 1, (iv) finally the results are compared to multi-objective optimal design. Ultimately, the advantages of this new isolation system are: (1) provide a physical limit switch to the isolation system in order to limit the maximum displacement of the mass; (2) reduce the effects of amplification dynamics in the resonance zone; (3) reduce the static displacement, all without possibly modifying the dynamic response in the isolation zone. • A new Vibro-Impact Control System integrating isolation, bumper and gap is defined. • Properly selecting parameters allows to beneficially exploit the occurrence of impact. • The study of the response scenarios is functional to identify optimal parameters. • The minimum acceleration criterion is proposed to select optimal parameters. [ABSTRACT FROM AUTHOR]

New technologies, such as additive manufacturing combined with topology optimisation or bio-inspired design, can produce lightweight structures with better dynamical properties but more complex geometries. Analysing these components with the finite element method can become time-consuming because of fine 3D meshes. By exploiting the node-dependent kinematic approach of Carrera's unified formulation and using Lagrange expanding functions, this work presents the implementation of adaptive finite elements for the free-vibration analysis of plates with an arbitrary thickness variation through the in-plane domain. In other words, the kinematics of the 2D model on which the element is based can be adapted to the geometry of the plate. The formulation is mainly based on the 3D integration of the approximating functions and computation of a 3D Jacobian matrix inside the element for the derivation of stiffness and mass matrices; substantially, the resulting elements are 3D elements in which the order of expansion through the thickness can be different from that in the plane of the plate. The free vibration analysis of some plates with different thickness variations is performed. The results demonstrate that the present elements allow us to accurately study these innovative 2D structures by employing much fewer degrees of freedom with respect to classical 3D finite elements. • Introduces a new class of 2D finite elements, the Adaptive finite elements. • These elements can study any type of variable thickness plate. • Validation of these new elements is performed. • Degrees of Freedom reduction is demonstrated. [ABSTRACT FROM AUTHOR]

Lamb wave-based structural health monitoring requires fast and accurate simulation tools for guided wave propagation in structures. In this article, a computationally efficient multiphysics time-domain spectral element (TDSE) model is presented for actuation, propagation, and sensing of Lamb waves in laminated composite strips (beams and panels) integrated with surface-bonded or embedded patch piezoelectric actuators and sensors. The transducers are physically modelled using an electromechanically coupled formulation, which combines an efficient layerwise zigzag theory for kinematics with a layerwise distribution for the electric potential field. The high-order TDSE has n physical nodes containing mechanical and electric degrees of freedom (DOFs) and a separate virtual electric node for modelling the transducers' equipotential surfaces with significantly reduced DOFs. The continuity of the displacement fields at the intersections (patch fronts) of the hybrid laminate integrated with patch transducers with the host laminate is maintained using the advanced hybrid point-least squares continuity model. The present guided wave predictions show excellent agreement with experimental measurements as well as continuum-based finite element solutions for isotropic and composite strips with surface-bonded piezo patches. The patch front continuity is shown to have a significant effect on the accuracy. The model is used to study the interaction of guided waves with the notch-type damage. The results establish the superiority of the proposed TDSE model over its standard two-node counterpart in terms of accuracy and efficiency. On the other hand, the equivalent single-layer theory-based model with the same number of DOFs yields highly erroneous predictions. • Presents an efficient multiphysics spectral element for smart composite strips. • First electromechanical spectral element based on an efficient layerwise theory. • Enforces continuity of nonlinear displacement field at piezo patch intersection. • Employs virtual electric node to satisfy equipotential conditions on piezo surfaces. • Enables fast, accurate simulation for Lamb wave-based structural health monitoring. [ABSTRACT FROM AUTHOR]

Quasi-zero-stiffness (QZS) isolators have shown great promise for low-frequency vibration isolation, thus outperforming conventional linear isolators. However, the hardening behavior typically exhibited in QZS isolators can deteriorate the isolation performance at high excitation amplitudes. To tackle this problem, utilizations of inherent material damping in soft resin offer a feasible way to counteract the hardening effect. This paper proposes a continuous QZS isolator, which can be readily fabricated by three-dimensional (3D) printing using soft resin. QZS properties are achieved by combining the snap-through behavior of inclined beams and the support of folded beams, acting as negative-stiffness (NS) and positive-stiffness (PS) elements, respectively. Analytical methods are developed for predicting the stiffness of the NS and PS elements of the design, whose efficacy is demonstrated numerically and experimentally through examining the static behavior. To evaluate the vibration isolation performance of the QZS isolator, a nonlinear single-degree-of-freedom (SDOF) model is proposed. The model incorporates cubic nonlinear damping in addition to classical viscous damping. The harmonic balance method (HBM) and the Runge-Kutta algorithm are employed to solve the equation of motion and to predict the velocity transmissibility. Parametric analyses are conducted to assess the effect of the excitation amplitude on isolation performance. The results show that an increased excitation level entails a down-shifting of the peak frequency in the transmissibility curve and that of the starting frequency of the effective isolation zone, resulting in enhanced isolation performance at large amplitudes. Numerical findings are further supported by dynamic experiments with varying excitation levels, demonstrating the validity of the proposed numerical model. [ABSTRACT FROM AUTHOR]

In this work, an adaptive shape optimization is developed using Geometry Independent Field approximaTion (GIFT) for 3D acoustics problems. The geometry-independent field approximation, using Non-uniform Rational B-splines (NURBS) to model the geometry, and Polynomial-splines over Hierarchical T-meshes (PHT-splines) to model the field space, are employed for 3D shape optimization problems in the context of time-harmonic acoustics. The adaptive optimization scheme proposed in this work combines a gradient-based optimization method with a local refinement algorithm. In this case, two types of local refinement algorithms are tested: a recovery-based and a residual-based algorithm. Single and multi-patch examples are studied, and it is shown that the proposed adaptive shape optimization scheme can lead to the same results as the uniform optimization, but using less time and fewer degrees of freedom. • Geometry Independent Field approximation (GIFT) is proposed for 3D shape optimization Helmholtz acoustic problems. • Geometry is modeled by NURBS while the physical domain is modeled by PHT-splines. • The proposed optimization scheme combines a gradient-based method with adaptive optimization. • Two different types of marking algorithms for the adaptive-refinement are tested: recovery-based and residual-based. • Shape optimization is performed over NURBS control points on the boundary. [ABSTRACT FROM AUTHOR]

• This article introduced the stiffness characteristics of the joint surface between the mechanical connection structures of the spindle-tool holder, tool holder-spring clamp, and spring clamp-tool of the spindle system in the robot machining system into the prediction of machining stability. • This paper proposed a method for establishing a tool tip frequency response prediction model for robot milling systems, which improves the accuracy of theoretical prediction of the tool tip dynamic characteristics of robot milling systems under different postures, Compared to the method of obtaining tool tip frequency response of robot milling system through experiments to support milling stability prediction, the method proposed in this paper effectively improves the efficiency of robot milling stability prediction. • The prediction results of the proposed tool tip frequency response prediction model were imported, and a two-degree-of-freedom chatter prediction model considering the regenerative effect is established, and the robot milling chatter is predicted considering redundant degrees of freedom. The accuracy of prediction results is verified by milling experiment. The change of tool tip frequency response caused by the posture dependence of robot dynamic is one of the key problems that make it difficult to accurately predict the milling stability of robot. In this paper, a tool tip frequency response prediction method considering the interface stiffness characteristics of spindle-tool system is proposed for stability prediction of robotic milling under the condition of posture variation. Firstly, the interface stiffness models of spindle-toolholder, toolholder-spring clip and spring clip-tool are established based on Yoshimura's unit area method. Then, The dynamics model for the robot body and the interface stiffness models for spindle-tool system are imported into the finite element analysis model of the spindle system, so that the prediction of the tool tip frequency response is realized by harmonic response analysis. Compared with the experimental results, the maximum error of the natural frequency was not more than 2 %, and the maximum error of the amplitude was not more than 12 %. Finally, the 2 DOF robot milling stability prediction model is established. Then the robot milling chatter is predicted considering redundant degrees of freedom from the perspective of regenerative chatter prediction theory, and the accuracy of prediction results is verified by milling experiment. [ABSTRACT FROM AUTHOR]

This work focuses on deriving guidelines for choosing structural theories for composite shells using Convolutional Neural Networks (CNN). The Axiomatic/Asymptotic Method (AAM) is used to evaluate higher-order structural theories' accuracy and computational efficiency based on polynomial expansions. AAM exploits the Carrera Unified Formulation to derive the finite element matrices and obtain natural frequencies. The outcomes of AAM concerning the accuracy and computational cost are used to train CNN for various composite shell configurations. The trained network can then be used as a substitute for finite element models to estimate the accuracy of a given structural theory. The results are provided via Best Theory Diagrams (BTD), in which the set of generalized displacement variables to retain the best accuracy can be read for a given amount of nodal degrees of freedom. Verification is carried out using results from FEM. The results proved the computational efficiency of CNN and highlighted the influence of the shell thickness for the proper choice of the structural theory. Third-order terms and transverse stretching are often necessary to obtain acceptable accuracy. • The accuracy of a structural theory is problem-dependent. • The selection process for the optimal modeling strategy can be a challenging task. • The synergistic use of machine learning and Carrera Unified Formulation can reduce the complexity of the selection process. [ABSTRACT FROM AUTHOR]

• A novel CMS method is proposed for the non-proportionally damped nonlinear systems. • Regarding the nonlinear interface forces as additional unknowns simplifies the synthesis procedure. • This method can preserve the intrinsic properties of nonlinear interface forces as much as possible. Engineering structures are generally designed based on linear elasticity assumptions. However, it is difficult to describe the connected structures using a simple linear system, due to factors such as sliding and friction at interfaces, and variations in contact areas during vibration processes. Therefore, it is necessary to develop an approach to tackle such systems with interface nonlinearities. In this paper, we proposed an extended free-interface component mode synthesis method. According to the proposed method, the substructures are separated at the nonlinear interfaces. Then the component mode synthesis procedure is carried out. By reasonably neglecting the contributions of higher order modes to the damping and inertia terms, it is demonstrated that the nonlinear interface forces and their time derivatives can be expressed as functions of themselves, as well as modal displacements and velocities. This characteristic facilitates the synthesis of the reduced order models for substructures in the state space. Also owing to this operation, the original properties of nonlinear interface forces can be preserved as much as possible, without any linearization. This method is suitable for non-proportionally damped structures with local nonlinearities such as mechanical structures with nonlinear spring and dashpot connections, rotor-bearing systems and so on. It also may be an alternative for the dynamic analysis of jointed structures with contact nonlinearities. Two numerical examples are presented to demonstrate the capability of the proposed method: (1) an eighteen degrees of freedom spring-dashpot-mass system with cubic spring and cubic dashpot interface connections is studied and (2) a more complex mechanical structure: a dual-rotor system with deep-groove ball bearing inter-shaft support. The numerical simulation results indicate that the dynamic responses of the reduced order model match very well with that of the full model, revealing the high accuracy of the proposed method with low computational costs. [ABSTRACT FROM AUTHOR]

• Constructing fractional-order foundation model for hydrogenerator unit. • Deriving nonlinear broadband dynamic equations for CSFS. • Discussing differences between CSFS and traditional single shaft system. • Analyzing the coupled dynamic performances of CSFS. The analysis of the coupled shaft-foundation system (CSFS) of a water turbine generator set is an extremely complicated task owing to its structural complexity and inherent nonlinear broadband dynamic characteristics. Thus, the coupling relationships of the CSFS remain unclear. The broadband vibration of the foundation subsystem has an evident influence on the vibration of the shaft subsystem of the unit; however, for the analysis of the dynamic characteristics of the water turbine generator, an overly complicated foundation can be reasonably simplified. To this end, this paper reports the development of novel energy-equivalent broadband modeling approaches to investigate the nonlinear vibration characteristics of CSFS. First, a relatively traditional integer-order lumped parameter model of the foundation subsystem was constructed, and its parameters were determined by fitting the response spectra obtained from an accurate hydropower house model. To improve the narrow-frequency limitation of the integer-order model and account for random disturbances, a novel fractional-order broadband modeling method is proposed. The advantage of the proposed fractional-order equivalent foundation model is that it can simultaneously reveal the broadband characteristics of complex structures at low frequencies of less than 1 Hz to high frequencies of hundreds of Hz with a single degree of freedom. Finally, coupled dynamic equations for the fractional-order CSFS model were derived and solved by considering the actions of various nonlinear factors and hydraulic pulsation excitation. A comparison of the dynamic responses of the CSFS with field test data demonstrated the effectiveness and practicability of the proposed modeling approaches. The results of the integer- and fractional-order CSFS models provide insights into the abundant dynamic laws and inner mechanisms of the nonlinear coupled dynamic system. Furthermore, they provided a reliable theory for the design and stability analysis of a hydropower unit, considering the varied vibrations of the coupled foundation. [ABSTRACT FROM AUTHOR]

Three significant tuning components in structural finite element model updating including objective function, optimization algorithm, and updating variables have a drastic influence on the accuracy of structural damage location diagnosis and intensity prognosis. These three components require both physical concepts and trial-and-error approaches. To assess damage in a structure accurately, the common information of several modes of the structure is required. The availability of higher modes data in engineering structures with a high degree of freedom is a complex task or even not practical in real cases. This study intends to propose a versatile objective function based only on the first vibration frequency and mode shape data. A new hybrid criterion called "Relative Discrepancy Function (RDF)" is proposed which is composed of relative differences of natural frequency and mode shape vector. Hereupon, the efficiency of the proposed identification method is evaluated through five sets including different robust objective functions and meta-heuristic optimization algorithms. These five damage identification sets are composed of three objective functions (Normalized Modal Strain Energy, Modified Total Modal Assurance Criterion, and RDF) and three optimization algorithms (Imperialist Competitive Algorithm, Teaching-Learning-Based Optimization algorithm, and the Most Valuable Player Algorithm (MVPA)). Subsequently, three truss and frame benchmark structures are assessed by means of five identification methods in single and multiple damage scenarios. It is observed that MVPA has both the fastest convergence rate and the lowest computational run time. Furthermore, the damage assessment results illustrate that when merely the first vibration mode data are used, the proposed identification method (RDF, MVPA) not only predicts the damage location properly, but also estimates the damage intensity successfully. • A new hybrid objective function for structural damage identification called "Relative Discrepancy Function (RDF)" is proposed. • The proposed objective function is based only on the first vibration frequency and mode shape data. • Most Valuable Player Algorithm (MVPA) has both the fastest convergence rate and the lowest computational run time. • The proposed identification method predicts the damage location and intensity successfully. [ABSTRACT FROM AUTHOR]

The present paper is focused on the analysis of the adhesion integrity of Single Lap Joints (SLJ). The technique adopted for the monitoring is based on the employment of vibration signals generated and received by piezo sensors attached on the specimens surfaces on the two opposite sides of the adhesive. Undamaged joints, when subjected to harmonic excitation, behave linearly exhibiting a spectral response including just the excitation frequency. As soon as the adhesive fails, harmonic excitation induces a rich variety of spectral components in the joints response, including subharmonics and superharmonics. A new approach is presented based on the beating resulting from the superposition of harmonic waves. The interpretation of the spectral content of the joint response is based on an analytical model of the single lap joint with different amounts of debondings associated with a nonlinear behaviour. Local Defect Resonance (LDR) conditions are promoted with the consequent superposition of defect with main structure vibration. Analytical results are compared with experiments and Finite Elements (FE) simulations demonstrating the consistence of the formulation. An efficient method for the Structural Health Monitoring (SHM) of the bonded single lap joints is provided, able to correlate the joint vibrational response to the debonding extension through the analysis of the response spectral content. • Beatings in the structural dynamic response of bonded Single Lap Joints (SLJ). • Simplified two degrees of freedom spring-mass model simulating SLJ. • Novel SHM method for the evaluation length of debonding. • Subharmonics and harmonics as indicator of damage. • Appearance of the defect first natural frequency according to the principles of LDR. [ABSTRACT FROM AUTHOR]

Frequency response functions (FRFs) are generally measured by investigating the input–output relationship of a target structure. An input is applied to the target structure and the output is measured. Typical vibration tests measure inputs as excitation forces using load cells or similar devices and outputs as velocities or accelerations using laser Doppler vibrometers or accelerometers. Each input or output has three translational degrees of freedom (DOF). Consequently, experimental models established based on such tests have three translational DOF. However, numerical models using finite element analysis (FEA) for existing structures have six DOF at each node (three translational and three rotational DOF). Therefore, numerical models using FEA and experimental models have gaps in their DOF, leading to diverse problems. This study realizes a non-contact measurement method for rotational DOF FRFs using an impulse excitation force generated by laser ablation (LA) where the input is a moment and the output is the velocity. A laser beam radiated from an Nd:YAG pulse laser emitter is divided using a half mirror, halving the laser pulse energy. Then, these laser beams are radiated on two points near a target structure's excitation point. The simultaneous occurrence of LA at these two points realizes a moment that acts on the target structure in a non-contact manner. This experiment uses a 5052 aluminum alloy plate where one end is fixed as a test piece. Both the auto FRFs and cross FRFs for the rotational DOF between two arbitrary points on the test piece are measured. The FRFs obtained by our method agree well with those obtained by FEA, demonstrating its efficacy. Image 1 • Realization of rotational frequency response function measurements based on laser ablation. • Establishment of a non-contact moment excitation system for vibration testing. • Demonstration of modal parameter identification from the measured rotational responses. • Investigation of the effects on the accuracy of rotational frequency response functions. [ABSTRACT FROM AUTHOR]

A two degree of freedom mass-spring-damper model on a moving lubricated belt is considered in this paper. The motions of the two masses are coupled through spring and damper and each mass interacts with a moving lubricated belt. The friction model includes the boundary, mixed and hydrodynamic regimes of lubrication contact regimes. Friction coefficient is presented as a function of sliding velocity at each mass interface that includes a combination of linear, exponential and cubic functions to account for relatively large coefficient at low sliding speed, followed by Stribeck effect at low to moderate speed ranges and finally a full hydrodynamic lubrication regime. A set of dimensionless parameters is introduced and system's dynamic response behavior as well as stability are studied for various combination of parameters. The results show that the unstable system response can be quasiperiodic, or periodic in the form of limit cycles away from the origin when the sliding velocity is relatively small. Triple and double periodic behavior is observed in addition to other responses when mass suspended to the ground is larger than the second mass. All responses become asymptotically stable when dimensionless sliding velocity threshold is exceeded. Finally, for a qualitative analysis, the method of averaging is used to solve the nonlinear coupled equations of motion in order to find the amplitude and frequency of steady-state vibration. A comparison between the numerical results from direct time integration and analytical findings shows that approximate solution is acceptable. [ABSTRACT FROM AUTHOR]

Assembled structures are nonlinear. The sources of this nonlinearity could include the jointed interfaces, damage and wear, non-idealized boundary conditions, or other features inherent in real parts. To study these systems and to ascertain if they will be operating in a regime in which the nonlinearity is prominent, nonlinear system identification techniques are needed to assess and characterize the nature of the nonlinearity in the structure. Significant progress over the last few years has focused on using nonlinear system identification to identify damage and other deviations from idealized structures. This research reviews nine different methods for nonlinear system identification (restoring force surface, Hilbert transform, direct quadrature, zero-crossing, short-time Fourier transform, Gabor wavelet, Morlet wavelet, Morse wavelet, and a neural network-based algorithm) in order to assess their accuracy. The methods are compared by identifying characteristics of two systems: a single degree of freedom model of a Duffing oscillator and measured data from a jointed structure. As neural networks are not commonly used for system identification, multiple variations of the method are investigated to study its effectiveness. Perturbation analysis is conducted to see the efficacy of the different methods for identifying parameters across a large range of design spaces, and the advantages and disadvantages of each method are discussed. The primary contribution of this paper is a comparison on both analytical and experimental data of multiple widely used system identification methods, and an assessment of when each method is most and least applicable, specifically in the context of jointed structures. [ABSTRACT FROM AUTHOR]

• A unified vibration modeling for open cylindrical shell-rectangular plate coupling structures under general coupling conditions is presented. • The model is reliable and effective, and its modeling process is more direct and convenient. • The presented model is appropriate for various boundary conditions. • The degrees of freedom of the presented model is significantly reduced than the traditional FEM. This paper presents a unified vibration modeling for free and forced vibration analysis of coupled open cylindrical shell-plate structures (COSPS). In the model, the coupled structure is first split into several open cylindrical shells and rectangular plates, and then based on Kirchoff's thin plate theory and Flügge's thin shell theory, the dynamic stiffness (DS) matrix of each substructure is separately established by applying the generalized superposition method and the projection method. Subsequently, according to the continuity and equilibrium conditions of the coupled boundary, the coordinate transformation matrix of each substructure is derived. After obtaining fundamental DS matrices and their coordinate transformation matrices, global DS matrices of various COSPS are assembled using a strategy similar to the finite element method (FEM) without repeating the theoretical derivation. To verify the convergence and reliability of the current formulation, free vibration and forced vibration analysis of three types of coupled structures are carried out, and the results are compared with those from published works and FEM solutions. In addition, an experimental model of a coupled structure is established and an experimental test is performed. The comparison results show that the proposed model is reliable and effective, and its modeling process is more direct and convenient. This work not only greatly expands the application scope of the DSM but also provides a new idea for the vibration analysis of COSPS. [ABSTRACT FROM AUTHOR]

This paper presents an investigation of the non-minimum phase (NMP) zeros in the single input single output (SISO) transfer function of three-DoF (degrees of freedom) damped flexible linear time-invariant (LTI) systems under the assumption of classical damping. It is well-known that when all the modal residue signs of any multi-DoF damped flexible LTI system are the same, NMP zeros never occur in the system dynamics for any value of system parameters including modal residue, modal frequency and modal damping ratio. However, when all the modal residue signs are not the same, then additional conditions in terms of the system parameters are required to guarantee the elimination of NMP zeros. In this paper, the zero loci of a three-DoF damped flexible LTI system are developed to derive the sufficient and necessary conditions for the elimination of all NMP zeros. These conditions can be employed in the robust physical design of flexible systems, i.e., as long as these conditions are satisfied, the elimination of NMP zeros is guaranteed even when the system parameters undergo variations. [ABSTRACT FROM AUTHOR]

This contribution presents the acoustical properties and corresponding theoretical descriptions of a Helmholtz resonator with an integrated cantilever inside the Helmholtz resonator neck. The advantage of this resonator design is a second resonance frequency, which leads to a supplemental frequency region with high sound absorption properties. An analytical model is derived to calculate the resonance frequencies and the absorption coefficient of the resonator system. This model has been verified with finite element simulations for the resonance frequencies, taking into account several geometric parameter variations. It has been validated experimentally for the calculated absorption coefficients by impedance tube measurements. In conclusion, it has been found a high influence of the geometric parameters on the resonance frequencies and a broader sound absorption performance of the coupled resonator system. • Helmholtz resonator with an integrated cantilever inside the resonator neck. • Helmholtz resonator with multiple resonance frequencies. • Analytical model considering Fluid–structure interaction. • Detailed study of coupling effect between the two resonance mechanism. • Two degree of freedom lumped element model. [ABSTRACT FROM AUTHOR]

• A novel Bayesian approach is presented to global mode shape identification with multiple setups. • A Chi-square distribution-based PDF is developed for MAC values. • Posterior covariance matrix is not influenced by the norm constraints. • The proposed method can be employed in case of closely spaced modes. • The effectiveness of the method is shown by numerical and experimental analysis. Modal identification of large-scale engineering structures may require multiple measurements obtained from different locations, due to the limitations in the instrumentation equipment. In such cases, the global values for modal frequencies and damping ratios can be estimated over the measurement setups by simply obtaining their statistical expected values. Estimation of global mode shape vectors, however, arises as a much more challenging problem since the local mode shapes confine at different degrees of freedom of the measured structure. To overcome this problem, a novel Bayesian methodology is presented in this study using a modal assurance criterion-based discrepancy model. By making use of this model, a novel solution procedure is presented to the existing literature, and mode shape normalization-based problems arising in the estimation of covariance matrix are solved. The computational efficiency of the proposed method is verified by two numerical and one real data example. The conducted investigations reveal that the presented methodology shows a good performance in terms of computational accuracy. [ABSTRACT FROM AUTHOR]

Load models that account for Human-Structure Interaction (HSI) may be preferable to accurately predict the dynamic response of lightweight footbridges subjected to pedestrian actions. Representing each person within a crowd may not be practical in engineering design calculations as time-variant models with a large number of degrees of freedom have to be managed. In addition, high computational time may be required to achieve the steady-state response. In this sense, this paper proposes a novel approach to calculate the vertical steady-state response of footbridges from a time-invariant coupled crowd-structure system. Considering the model of the structure and a feedback model of the crowd, a total closed-loop Transfer Function (TF) of the coupled system is derived. Based on this frequency-domain interacting methodology, a step-by-step procedure is set to asses the vibration serviceability of lightweight footbridges due to harmonic excitations through simple algebraic operations. The proposal is used to study a Fibre Reinforced Polymer footbridge subjected to two streams of walking pedestrians. For this structure, a good compromise between experimental and numerical results is obtained in terms of vertical vibrations and TFs. To further validate the proposed approach, a pre-stressed concrete laboratory facility is also analysed, obtaining a satisfactory agreement between the experimental and numerical TFs. Thus, the proposed approach allows to evaluate lightweight footbridges under crowd-induced loads considering HSI in a simple and accurate manner, which is clearly geared to practice. [ABSTRACT FROM AUTHOR]

• The dovetailed blade model considering interface pressure distribution characteristics. • The model reduction method for preserving local contact features. • Micro-slip phenomenon of contact interface captured by dense macro-slip contact element. • Equivalent treatment of contact surface pressure and aerodynamic excitation. • Improved design of tenon structure parameters. A dynamic model of a tenoned rotating blade considering the pressure distribution characteristics of the contact interface is established and the degree of freedom of the model is reduced by the double coordination free-interface modal synthesis method in this paper. Firstly, the finite element model of the blade is established by ANSYS and the finite element matrix is extracted. Subsequently, multiple contact pairs were established on the contact surface of the tenon to capture the micro-slip characteristics of the contact interface. The normal pressure of the contact pair is obtained by the ANSYS blade-disk contact prediction and load equivalence to take the pressure distribution characteristics into account in the blade dynamics analysis. Then, non-uniform aerodynamic excitation is applied to the blade to simulate the load on the blade under real working conditions. Finally, the double coordination free-interface modal synthesis method is used to reduce the degree of freedom. Due to the coordination condition of the force and displacement of the substructure connection interface, the degree of freedom of the substructure interface is directly reduced. The final reduced degree of freedom is only the sum of the retained modes of the substructure, which greatly improves the computational efficiency. The dynamic equation is solved by the time integration method, and the effects of the tenon angle, rounded corner, and friction coefficient are discussed. The results show that the double coordination free-interface modal synthesis method can greatly reduce the degree of freedom of the tenon-connected blade model under the premise of ensuring accuracy while retaining the local contact characteristics of the contact interface. The structural parameters of the dovetail structure have a great influence on the vibration reduction characteristics of the blade. When designing the tenon structure, it is necessary to pay attention to these parameters. [ABSTRACT FROM AUTHOR]

Abstract Experimental system identification through modal analysis is often conducted by assuming linear constitutive laws and kinematic relationships. Significant prediction errors from these identified models can occur when the amplitude dependent contribution of nonlinearities is ignored. In this paper, the impact of such nonlinearities on the parameter identification and accuracy of a linear model is shown to depend significantly on the experimental procedures. Using modal analysis techniques and focusing on vibration near the fundamental mode, a cantilevered beam is modeled as a single degree of freedom oscillator with parameters to be determined through experimental system identification. Various testing procedures are described in detail and used to demonstrate the impact of nonlinearities on the outcome of different system identification processes. The signal control methods compared are (1) open loop, (2) constant input, and (3) constant response excitation. Forcing types considered are single point and distributed. Nonlinearities in experimental response are shown for all procedures, and it is demonstrated that the observed character and degree of the nonlinearities vary depending on the testing procedure. The paper makes various recommendations for experimental system identification procedures using linear structural models, which include developing empirical models for parameter shifts due to nonlinearities and using constant response tests to minimize nonlinear effects in the measured system response. By implementing these identification methods, parameter variations can be included in the linear model to significantly reduce predicted response and parameter errors for weakly nonlinear second-order systems. [ABSTRACT FROM AUTHOR]

Abstract Stability investigations of general non-conservative parametrically excited systems with asynchronous excitation are presented. Focusing on the global stability effects outside of the traditional resonance areas, systems with two degrees of freedom are considered featuring displacement- and/or velocity-proportional parametric excitation with variable phase relations. In particular, facing the lack of studies on this subject, special attention is paid to time-periodic systems containing gyroscopic and circulatory terms. Through the application of the semi-analytical method of normal forms, general conditions for the appearance of possible global effects are derived. Apart from the "total instability" – presently the only known global effect – new stabilizing and destabilizing effects affecting the stability over the whole range of excitation frequencies are discovered. The derived conditions show, that such global effects are expected to be rather common in complex mechanical system, especially those, featuring circulatory terms. The qualitative analytical results are also confirmed by numerical stability analysis based on Floquet theory. As a mechanical example a minimal model of a squealing disk brake is examined. It is shown that this complex model is indeed subject to parametric excitation leading to global stability effects. These findings may contribute to a better understanding of the squealing phenomenon. Further, the newly obtained knowledge may as well be utilized for extended vibration suppression in mechanical systems in the context of parametric anti-resonance. [ABSTRACT FROM AUTHOR]

Abstract This paper reports findings from an experimental study on vortex-induced vibration of a horizontal, flexibly-mounted cylinder positioned near the free surface of fluid flow. The cylinder is allowed to oscillate in the vertical direction only. Oscillation amplitude and frequency data are presented as a function of reduced velocity and dimensionless depth from the free surface. Data are presented for cases of decreasing depth from where the resting cylinder is fully-submerged until its centerline is even with the free surface of the water. For a fully-submerged cylinder, VIV behavior is consistent with published findings of similar systems, producing a well-documented lock-in region with initial, upper, and lower branches. Broadly, as the cylinder is raised from the fully-submerged case, the amplitudes diminish and the lock-in region decreases in range and shifts toward higher reduced velocities. When the cylinder is very near the surface, a second region of oscillations occurs at higher reduced velocities. This region emerges in cases where the cylinder's top edge is half a diameter below the free surface. For a short range of depths, the lock-in region and the non-zero amplitude region at higher reduced velocities coexist. But after a critical depth, the lock-in region disappears and oscillations are observed only at the higher reduced velocity region. Multi-frequency oscillations and regions of hysteresis are observed for some cases of low depth and high reduced velocity. [ABSTRACT FROM AUTHOR]

Abstract This paper presents an approach to calculate the natural frequency and frequency response function (FRF) statistics of structures connected to attachments at uncertain locations. The main structure is divided into two regions to which the attachment can, or cannot, be connected. The approach is based on component mode synthesis analysis of finite element models of these regions. Multi-point constraints are used to connect the attachment to the main structure to avoid the need to re-mesh the structure. The use of characteristic constraint modes is used to reduce the number of interface degrees of freedom (DOFs) and hence reduce the computational cost further. One or more baseline systems, for which the attachment is connected at a given position, are analysed and the eigensolution found. A perturbation is then applied to the baseline solution to estimate the solution for other attachment locations. The method can be applied to any problem requiring multiple re-analysis. Here, emphasis is placed on probabilistic approaches using Monte Carlo Simulation (MCS), and the natural frequency and FRF statistics are then estimated through MCS. To illustrate the approach, numerical results are presented for a beam and a plate with a randomly attached mass and a plate with an attachment with a number of internal and attachment DOFs. Numerical results are compared with experimental measurements for the cases of a beam and a plate with an attached mass. The results indicate that the method provides accurate predictions at a significantly reduced computation cost when compared to multiple direct solutions. [ABSTRACT FROM AUTHOR]

Abstract This paper proposes an analytical vibration model of a disk resonator gyroscope (DRG) based on the wave propagation theory, which can predict the key specifications of a DRG rapidly and accurately before fabrication, and can be employed in design optimization. This wave propagation analysis is based on the ray tracing method (RTM) which considers wave propagation and scattering in the formulation. In the RTM, wave transmission and reflection coefficients are the key issues that must be accurately predicted. A novel C-joint is proposed to predict these key coefficients between the rings and spoke with high precision and short estimated time. To verify the soundness of the proposed model, a tentative vibration model for a double-ring (the basic element of a DRG) is established by the RTM and compared with the 3D finite element (FE) model. The two models show excellent agreements in natural frequencies, trend predictions and harmonic displacements. Then, the proposed model is expanded to a multi-ring practical DRG. In addition, taking the advantage of the symmetry in the DRG, the substructuring and recursive methods are employed to reduce the computational overhead. The numerical experiments show that the proposed analytical vibration model for a DRG meets well with the 3D FE model. For instance, the differences between the calculated resonant frequencies from the 3D FE model and the analytical model are less than 3%. After fabrication, the measured average resonant frequency of the prototypes deviates 6.7% from that of the theoretical prediction. [ABSTRACT FROM AUTHOR]

Abstract The present paper proposes a novel adaptive passive stiffness (APS) device which can produce variable stiffness in an adaptive fashion. This APS device consists of four springs arranged in a rhombus configuration and a guidance template. The stiffness of the device is controlled through varying the angle of the rhombus configuration. The function of the guidance template is to relate the angle of the rhombus to the targeted system response such that the stiffness can be varied in an adaptive manner, without the need for feedback or external energy. Two analytical models are developed to capture the behavior of the APS device which shows good agreement with the experimental data. Experimental result indicates that the proposed APS device can produce adaptive stiffness as expected. A cubic nonlinearity is produced and deployed in a single-degree-of-freedom (SDOF) system to form a hardening Düffing oscillator. Dynamic tests show that the experimental characteristics of the Düffing system agrees well with the numerical results, thereby demonstrating that the APS device is effective in producing smoothly and continuously adaptive stiffness in an adaptive fashion. In addition, a fourth order even function is used as the guidance template to produce a softening-hardening adaptive stiffness. The performance of this adaptive stiffness is numerically evaluated for seismic protection. It is found that the structural responses can be reduced effectively when using this softening-hardening adaptive stiffness. The key value of this APS device is that the guidance template can be easily changed to any desired continuous function such that the targeted adaptive stiffness can be obtained. This provides possibility for controlling the vibrations of structures in a passively adaptive manner. Highlights • A novel adaptive passive stiffness (APS) device is proposed, modeled and tested. • Theoretical models have been developed to characterize the behavior of the device. • Experimental results show that the APS device can produce smooth and continuous nonlinear stiffness in an adaptive fashion. • Numerical results show that the produced softening-hardening stiffness is effective for seismic protection. [ABSTRACT FROM AUTHOR]

Abstract A new method is developed for direct damping matrix identification using experimental receptance-matrix data together with physical connectivity constraints based on what are described as layers. A number of spectral lines are considered in symmetric frequency bands around the damped peaks of the receptances and the identification procedure is shown to be ill-conditioned (singular) when one of the spectral lines coincides with an undamped natural frequency. A test is developed that makes use of a stabilisation diagram to ensure not only that a solution exists, but also that it is stable when the number and frequency range of the spectral lines is changed. An experimental parametric three degrees of freedom lumped mass system connected by springs and air dampers is considered and the matrix of non-proportional viscous damping terms is identified under different damper configurations and levels. Highlights • A method for damping matrix identification from experimental receptance data is presented. • Physical constraints are imposed on the identification using the described Layers. • Stable quantification of damping is ensured and a new stability diagram is introduced. • The identified damping matrix is the closest to the real one. • Experimental validation on a parametric damped three degrees of freedom lumped system is provided. [ABSTRACT FROM AUTHOR]

Abstract A novel type of a nonlinear energy sink is proposed by introducing a lever to reduce the necessary mass. The lever-type nonlinear energy sink is attached to a two-degree-of-freedom simplified model of whole-spacecraft subjected a harmonic excitation. The transmissibility is used to evaluate the performance of vibration reduction. The harmonic balance method with an alternating frequency time is applied to predict the variation of the transmissibility with the excitation frequency. The harmonic balance solutions are supported by the numerical results. It is found that the disappearance of closed detached resonance response may dramatically decrease the transmissibility. Besides, the quasi-periodic motion may be a predictor to generate the closed detached resonance. The harmonic balance solutions are used to examine the effects of the mass, the nonlinear stiffness and the fulcrum location. With a suitable fulcrum location, the lever-type nonlinear energy sink outperform a conventional nonlinear energy sink with same mass, damping and nonlinear stiffness. [ABSTRACT FROM AUTHOR]

Abstract In this paper, the vibration energy transfer mechanism of the single-sided vibro-impact (SSVI) nonlinear energy sink (NES) is studied. The concept of impact mode is proposed where the device velocities are decomposed into an energy free impact mode (EFIM) and an energy dissipation impact mode (EDIM). The impact modes are applied to the analysis of a single-degree-of-freedom (SDOF) vibration system with a SSVI NES. This analysis shows that the energy in the system can be redistributed between the different impact modes and that energy transferred from the EFIM to the EDIM is beneficial, because portions of the energy in the EDIM will be dissipated by impact, while the energy in the EFIM will not. More importantly, the mechanism of the SSVI NES to realize the local dissipation of energy is revealed. Furthermore, in order to better evaluate the energy dissipation performance of the SSVI NES, a new evaluation criterion called the vibro-impact vibration reduction (VVR) factor is proposed. Then, the relationship between the VVR factor and the energy free impact mode coefficient is investigated using the Hilbert transform. Finally, the effect of the SSVI NES parameters on the energy dissipation performance of the SSVI NES with various initial conditions is discussed, and a satisfactory region for the SSVI NES design, which is identified via numerical simulation, is proposed. Highlights • Impact modes are proposed and applied to investigate the system with a single-sided vibro-impact nonlinear energy sink. • The energy transfer mechanism of the SSVI NES is revealed. • The vibro-impact vibration reduction factor is proposed to evaluate the energy dissipation performance of the SSVI NES. • The influence of parameters on the NES performance is discussed and a satisfactory region for SSVI NES design is obtained. [ABSTRACT FROM AUTHOR]

Abstract The discontinuity mapping technique provides quite a good way to study the near-grazing dynamics in the impacting oscillators. However, disagreements between the results obtained by the discontinuity mapping technique and the direct numerical observations still exist in terms of modeling and stability analysis. In particular, when applying the existing theory to deal with the complicated degenerate or other co-dimension two grazing bifurcations, even potential mistake in the qualitative analysis might arise. To reduce such disagreements, the local zero time discontinuity mapping is extended to higher order terms for the generic multi-degree-of-freedom impacting oscillators under harmonic excitation in this paper. Furthermore, to demonstrate the necessity and feasibility of using the higher order zero time discontinuity mapping for the analysis of degenerate grazing bifurcation, comparisons between the lower and higher order truncation are made through the existence analysis of near-grazing impact periodic motions. Highlights • The existing local zero time discontinuity mapping is extended to higher order terms. • Comparisons between the lower and higher order truncation are presented. • The necessity of higher order discontinuity mapping for degenerate grazing is shown. [ABSTRACT FROM AUTHOR]

Abstract This paper presents a novel Tunable Vibration Absorber with Liquid Elastic Chamber (TVA-LEC) for structural vibration suppression. It is formed by covering a rigid cylindrical chamber with two rubber membranes that act as springs and filling the chamber with incompressible liquid. Compared to conventional TVAs, the TVA-LEC is cost and weight efficient when it is integrated to the liquid network of a primary structure, such as oil pipelines inside aircraft wings, by utilizing the existing liquid as the mass of the TVA. A single-degree-of-freedom (SDOF) analytical model is developed for the proposed device with discussions on the tuning of its natural frequency. It is revealed that the natural frequency of the TVA-LEC can be tuned by regulating the liquid mass. The analytical model is validated by experimental tests in which the TVA-LEC is installed on a cantilever beam and the liquid mass is adjusted. The natural frequency of the TVA-LEC device shifts from 16.99 Hz to 21.99 Hz by adding liquid, which agrees well with the analytical prediction. Highlights • A novel tunable vibration absorber with liquid elastic chamber is proposed. • The elastic membrane acts as spring and liquid sealing. • The natural frequency of the absorber is tuned by regulating the liquid mass. • A simplified expression relating the natural frequency to this device's physical parameters is presented. [ABSTRACT FROM AUTHOR]

Abstract Presented here is a theoretical study on basic subunits of the elastic metamaterial used for vibration and sound mitigation. The subunit of the material is modeled as a mass-in-mass two degree of freedom excited system where the mass-nonlinear spring system is used as a vibration absorber. The nonlinearity in the system is of power type and the excitation force is a general time-periodic function. The motion is described with two coupled second order nonlinear and nonhomogeneous equations. The novelty in the paper is the newly developed analytical procedure for approximate calculation of the response of a power-type nonlinear coupled conservative and non-conservative two degree-of-freedom system subjected to generally time-periodic forcing given in the form of the Ateb function. In addition, based on the known concept of 'effective mass' for the linear vibration absorber, the 'effective mass' for the nonlinear vibration absorber is developed. It is obtained that the effective frequency bandwidth for the suggested nonlinear mass-in-mass system is much larger than for the linear one. For the nonlinear system the frequency stop-band area of vibration tends to be continual. The results are proved numerically and experimentally. [ABSTRACT FROM AUTHOR]

The recently developed Wiener Path Integral (WPI) technique for determining the joint response probability density function of nonlinear systems subject to Gaussian white noise excitation is generalized herein to account for non-white, non-Gaussian, and non-stationary excitation processes. Specifically, modeling the excitation process as the output of a filter equation with Gaussian white noise as its input, it is possible to define an augmented response vector process to be considered in the WPI solution technique. A significant advantage relates to the fact that the technique is still applicable even for arbitrary excitation power spectrum forms. In such cases, it is shown that the use of a filter approximation facilitates the implementation of the WPI technique in a straightforward manner, without compromising its accuracy necessarily. Further, in addition to dynamical systems subject to stochastic excitation, the technique can also account for a special class of engineering mechanics problems where the media properties are modeled as stochastic fields. Several numerical examples pertaining to both single- and multi-degree-of-freedom systems are considered, including a marine structural system exposed to flow-induced non-white excitation, as well as a bending beam with a non-Gaussian and non-homogeneous Young's modulus. Comparisons with Monte Carlo simulation data demonstrate the accuracy of the technique. [ABSTRACT FROM AUTHOR]

A model-updating approach based on an improved free-interface component mode synthesis method is proposed. First, the equivalent higher-order matrix of the system is developed using a set of linearly independent vectors to capture the effects of the neglected higher-order modes. Second, the perturbation method is applied to derive the change for both eigenvalues and eigenvectors of each component while implementing a modification to the updated finite element model. The perturbation for both the eigenvalues and eigenvectors of each component are used to formulate the synthesis equations containing the perturbation expression. Next, the model-updating process is conducted using the synthesis model for which the degrees of freedom have been greatly reduced. The reduction in the total degree of freedom speeds up the solution process for the model-updating problem. Finally, the computational efficiency and accuracy of the presented method is demonstrated using a wing structure and by modal testing of a bolted plate. [ABSTRACT FROM AUTHOR]

We present an experimental study on the vortex-induced vibration (VIV) of a low mass-damping one-degree-of-freedom circular cylinder subject to uniform cross-flow, with pairs of control rods of varying size located in its wake. Two particular locations for control rods, selected according to recent experimental maps of VIV sensitivity to localized perturbations, have been tested for increasing control rod diameters, d . Important amplitude reductions are observed for all arrangements investigated, with nearly total suppression of oscillations (up to 90 % ) for control rods of d  = 0.4 D , where D is the diameter of the main cylinder. Force measurements have been used to describe the nature of changes observed in the wake and the mechanisms behind the VIV control. In general, the placement of control rod pairs in the near wake leads to an important weakening of the lift coefficient and alters substantially the phase between transverse force and cylinder displacement. Moreover, it is shown that, for some particular arrangements, attenuation of VIV is obtained along with a drag reduction of approximately 60 % at the upper branch of amplitude response, rendering the present strategy an interesting and practical solution for VIV control when several cylinders need to be installed together. [ABSTRACT FROM AUTHOR]

A numerical approach is proposed to compute the dynamic response of periodic structures with cyclic symmetry, and assemblies made up of these periodic structures. The wave finite element (WFE) method is used to describe the wave modes which occur around the circumferential direction of these periodic structures. Emphasis is placed on assessing the dynamic flexibility modes of a periodic structure by considering unit forces which are successively applied to the boundary degrees of freedom. It is shown that the matrices of dynamic flexibility modes can be quickly computed. This yields an efficient dynamic substructuring technique to analyze the dynamic behavior of assemblies made up of several periodic structures. Numerical experiments are carried out which concern the analysis of a single periodic structure as well as assemblies made up of two and three structures. [ABSTRACT FROM AUTHOR]

This paper focuses on the performance of the two two-loop implicit sparse matrix numerical integration (TLISMNI) methods as the numerical solution of index-3 differential algebraic equations (DAEs) of motion arising in stiff multibody dynamics with contact and constraint. The original TLISMNI method proposed for the first time by Shabana and Hussein uses the Newmark method or Hilber/Hughes/Taylor (HHT) method as the implicit integration algorithm [TLISMNI (Newmark/HHT) method]. These two integration algorithms consider the accelerations and Lagrange multipliers as basic unknowns and their numerical accuracy is no more than order 2. In order to have a higher integral precision, we propose a new two-loop implicit procedure based on an extended backward differentiation formula scheme [TLISMNI (EBDF) method] which considers coordinates and velocities as basic unknowns. The whole structure of this proposed method is different from the traditional one due to the different unknowns. Furthermore, we apply these two kinds of methods, TLISMNI (Newmark/HHT) method and TLISMNI (BDF/EBDF) method, to the contact and constraint problems of flexible multibody dynamics while few studies of TLISMNI methods have been done on these non-smooth problems. The Baumgarte method and HHT- α method are also used to solve the same contact and constraint problem, and the advantages and disadvantages of all these methods above are compared in this study. Results show that the proposed method only needs to perform less iterations to satisfy the same tolerance of error than the TLISMNI (HHT) method does. In some cases the Baumgarte method and HHT- α method cannot give reasonable results while the TLISMNI methods perform well when the contact and constraint problems are involved. Moreover, the numerical experiment also indicates that the numerical damping property of the HHT method employed in both the TLISMNI method and the GGL formulation (used in the HHT- α method) can behave in a different way to damp out high frequency oscillations induced by impact. [ABSTRACT FROM AUTHOR]

The paper studies the transverse nonlinear vibration of an isotropic and homogeneous annular membrane spinning at constant angular velocity, under the action of a uniform transverse load. The equilibrium configuration of the membrane, clamped along the inner edge and free along the outer edge, and the natural frequencies of vibration of the membrane are calculated. A Galerkin procedure is used to determine a reduced order model describing the weakly nonlinear vibration of the membrane, and it is shown that near-resonance vibration can be modeled as a single degree of freedom Helmholtz-Duffing oscillator. A detailed study at vibration frequencies close to the fundamental, axisymmetric vibration mode shows a transition from softening to hardening behavior, and jump phenomena or hysteretic behavior depending on the angular velocity, the transverse load, the amplitude of dynamic excitation and the damping ratio. The results are in agreement with dynamic implicit finite element simulations in Abaqus/Standard and direct experimental measurements. [ABSTRACT FROM AUTHOR]

• An iterative method is developed for the joint with many interface DOFs. • The iterative method is also extended for nonlinear joint identification. • The identification of the end-toothed connection was conducted. • Simulation and experiment were in good agreement. Accurate identification of mechanical connections plays a significant role in predicting the dynamic behaviors of assembled structures. Traditional identification methods based on frequency response function (FRF) decoupling may not be suitable for the joints with many interface degrees of freedom (DOFs), especially in the case of insufficient measured FRF data and large experimental noise. In this paper, a new iterative method is proposed to solve this problem. First, the incremental basic formulas on the measured DOFs and pseudo-measured DOFs are derived, respectively. The former avoids the measurements of rotational or interface DOFs whereas the latter is suitable for the identification of the joint with many interface DOFs. Then, the joint properties expressed in terms of mass, stiffness and damping matrices are updated from the solution of the linear equation system combined with the iterative basic identification equations at different frequencies. Thus, the original problem is transformed into estimating the parameters iteratively by minimizing the differences between predicted responses and measured ones, which effectively improves the identification accuracy and numerical stability. Moreover, the iterative method is extended to the identification of nonlinear joints based on describing function theory. The validity and superiority of the proposed method are verified by a simple lumped parameter system. Then, a numerical example of a structure connected with bolted joints, which has a large number of interface DOFs, is simulated to verify the convergence and the robustness of the method to noise. Finally, the joint dynamic properties of an end-toothed connection under different contact states are identified, and the assembly responses are also accurately predicted. The effectiveness and the applicability of the proposed iterative identification method to the real structures are well validated. [ABSTRACT FROM AUTHOR]

• Bayesian model updating using complex modal data. • MPVs and posterior statistics of the complex modal data are considered. • Development of posterior PDF using dynamic condensation of the system. • An MWG sampler is proposed for sampling from the posterior PDF. • An alternative methodology is proposed based on the TMCMC sampler. An approach for the Bayesian model updating of a linear dynamic system using complex modal data identified from dynamic test data is proposed in this paper. Very few works have utilized complex modal data for Bayesian model updating, and these works consider only the Most Probable Value (MPV) of the modal parameters as the modal data. On the other hand, the present work considers the posterior uncertainties of the modal parameters along with the MPVs as the modal data. Additionally, dynamic reduction has been applied to downsize the full system model to a reduced model with master Degrees of Freedom (DOFs) of the reduced model confined to the observed DOFs. Dynamic reduction facilitates updating of structural parameters without the requirement of mode matching. Additional uncertain parameters in the form of system modal frequencies, damping ratios, and partial mode shapes are introduced to establish a link between the structural model parameters and the modal data through the eigenvalue equation. Detailed formulation leading to the development of the posterior Probability Density Function (PDF) is presented, and a new Metropolis-within-Gibbs (MWG) sampler is proposed to simulate samples from the posterior PDF. Furthermore, a formulation is presented for evaluating the probability of damage based on the posterior samples obtained using the proposed approach from the structure's undamaged and possibly-damaged state. The proposed approach is validated and demonstrated comprehensively through simulated examples and an experimental study. Lastly, the performance of the proposed approach is compared with an alternative approach which is developed by integrating out the partial system mode shape from the posterior PDF. [ABSTRACT FROM AUTHOR]

The two-field vibroacoustic finite-element (FE) model requires a relatively large number of degrees of freedom compared to the monophysics model, and the conventional force identification method for structural vibration can be adjusted for multiphysics problems. In this study, an effective inverse force identification method for an FE vibroacoustic interaction model of an interior fluid–structure system was proposed. The method consists of: (1) implicit inverse force identification based on the Newmark- β time integration algorithm for stability and efficiency, (2) second-order ordinary differential formulation by avoiding the state-space form causing large degrees of freedom, (3) projection-based multiphysics reduced-order modeling for further reduction of degrees of freedom, and (4) Tikhonov regularization to alleviate the measurement noise. The proposed method can accurately identify the unmeasured applied forces on the in situ application and concurrently reconstruct the response fields. The accuracy, stability, and computational efficiency of the proposed method were evaluated using numerical models and an experimental testbed. A comparative study with the augmented Kalman filter method was performed to evaluate its relative performance. • Implicit force identification method for vibroacoustic system is proposed. • Vibroacoustic FE model and its recent reduction technique are implemented. • Inverse force identification process is derived from the Newmark-beta method. • Tikhonov regularization is here employed to alleviate the measurement noise. • The performance of the method is numerically and experimentally evaluated. [ABSTRACT FROM AUTHOR]

• A numerical model able to VIV on a circular cylinder is presented. • The model parameters are defined by using a genetic algorithm-based approach • Results of the model are discussed and compared to experimental data • The idea is to define a model for VIV usable for civil applications. The paper presents a numerical model, based on the equivalent oscillator approach, able to simulate vortex induced vibrations on a circular cylinder. This model consists of a single degree of freedom mechanical system characterized by non-linear parameters that reproduce the fluid-structure interaction in time domain. A genetic algorithm approach was used in order to identify the characteristic parameters of the equivalent oscillator: obtained results are discussed and compared with wind tunnel experimental data and with a previous version of the numerical model. Comparison is performed both in terms of aerodynamic forces and oscillation amplitudes and both in steady and transient conditions. [ABSTRACT FROM AUTHOR]

As the number of degrees of freedom (DOFs) in structural dynamic problems becomes larger, the analyzing complexity and CPU usage of computers increase drastically. Condensation (or reduction) method is an efficient technique to reduce the size of the full model or the dimension of the structural matrices by eliminating the unimportant DOFs. After the first presentation of condensation method by Guyan in 1965 for undamped structures, which ignores the dynamic effects of the mass term, various forms of dynamic condensation methods were presented to overcome this issue. Moreover, researchers have tried to expand the dynamic condensation method to non-classically damped structures. Dynamic reduction of such systems is far more complicated than undamped systems. The proposed non-iterative method in this paper is introduced as 'Maclaurin Expansion of the frequency response function in Laplace Domain' (MELD) applied for dynamic reduction of non-classically damped structures. The present approach is implemented in four numerical examples of 2D bending-shear-axial frames with various numbers of stories and spans and also a floating raft isolation system. The results of natural frequencies and dynamic responses of models are compared with each other before and after the dynamic reduction. It is shown that the result accuracy has acceptable convergence in both cases. In addition, it is indicated that the result of the proposed method is more accurate than the results of some other existing condensation methods. [ABSTRACT FROM AUTHOR]

Based on a multiple degrees of freedom dynamic model of a vehicle powertrain system, natural vibration analyses and sensitivity analyses of the eigenvalues are performed to determine the key inertia for each natural vibration of a powertrain system. Then, the results are used to optimize the installation position of each adaptive tuned vibration absorber. According to the relationship between the variable frequency torque excitation and the natural vibration of a powertrain system, the entire vibration frequency band is divided into segments, and the auxiliary vibration absorber and dominant vibration absorber are determined for each sensitive frequency band. The optimum parameters of the auxiliary vibration absorber are calculated based on the optimal frequency ratio and the optimal damping ratio of the passive vibration absorber. The instantaneous change state of the natural vibrations of a powertrain system with adaptive tuned vibration absorbers is studied, and the optimized start and stop tuning frequencies of the adaptive tuned vibration absorber are obtained. These frequencies can be translated into the optimum parameters of the dominant vibration absorber. Finally, the optimal tuning scheme for the adaptive tuned vibration absorber group, which can be used to reduce the variable frequency vibrations of a powertrain system, is proposed, and corresponding numerical simulations are performed. The simulation time history signals are transformed into three-dimensional information related to time, frequency and vibration energy via the Hilbert-Huang transform (HHT). A comprehensive time-frequency analysis is then conducted to verify that the optimal tuning scheme for the adaptive tuned vibration absorber group can significantly reduce the variable frequency vibrations of a powertrain system. [ABSTRACT FROM AUTHOR]

Parametric non-linear vibrations of flexible cylindrical panels subjected to additive white noise are studied. The governing Marguerre equations are investigated using the finite difference method (FDM) of the second-order accuracy and the Runge-Kutta method. The considered mechanical structural member is treated as a system of many/infinite number of degrees of freedom (DoF). The dependence of chaotic vibrations on the number of DoFs is investigated. Reliability of results is guaranteed by comparing the results obtained using two qualitatively different methods to reduce the problem of PDEs (partial differential equations) to ODEs (ordinary differential equations), i.e. the Faedo-Galerkin method in higher approximations and the 4th and 6th order FDM. The Cauchy problem obtained by the FDM is eventually solved using the 4th-order Runge-Kutta methods. The numerical experiment yielded, for a certain set of parameters, the non-symmetric vibration modes/forms with and without white noise. In particular, it has been illustrated and discussed that action of white noise on chaotic vibrations implies quasi-periodicity, whereas the previously non-symmetric vibration modes are closer to symmetric ones. [ABSTRACT FROM AUTHOR]

Eigenvalues and eigenvectors play a fundamental role in determining the dynamic behavior of a vibrating system. Thus, an important goal in vibration control is to modify the eigenstructure to match the design specifications. Feedback control is a popular approach to this problem, which is however not always satisfactory. In fact, while system controllability suffices to assure that any requirement on the eigenvalues can be met by the controlled system, desired closed-loop eigenvectors cannot be attained in general, due to inherent limitations of active control. To overcome such a problem, this paper proposes a hybrid approach in which the mechanical system and the controller are concurrently designed to improve the attainability of the desired eigenstructure. Indeed, the suitable modification of the system inertial and elastic parameters modifies the set of eigenvectors that can be achieved through active control. In this work is demonstrated that such an objective can be effectively accomplished by minimizing the rank of a certain matrix which depends on the features of the original system and on the desired eigenpairs. Two algorithms for rank minimization are described and adjusted for the problem under consideration. The method is validated with three examples. In the first one, eigenstructure assignment of a 5 degrees of freedom system that previously appeared in the literature is performed, demonstrating the effectiveness of the proposed approach with respect to the state of the art. In the second example the same 5 degrees of freedom system is considered by also including damping, to evaluate the method capability to deal with damped systems. The third one is a 30 degrees of freedom system that enables the comparison of the two algorithms for different choices of the actuation. [ABSTRACT FROM AUTHOR]

The Harmonic Balance Method (HBM) is a frequency-domain based approximation approach used for obtaining the steady state periodic behavior of forced dynamical systems. Intrinsically these systems are non-autonomous and the method offers many computational advantages over time-domain methods when the fundamental period of oscillation is known (generally fixed as the forcing period itself or a corresponding sub-harmonic if such behavior is expected). In the current study, a modified approach, based on He's Energy Balance Method (EBM), is applied to obtain the periodic solutions of conservative systems. It is shown that by this approach, periodic solutions of conservative systems on iso-energy manifolds in the phase space can be obtained very efficiently. The energy level provides the additional constraint on the HBM formulation, which enables the determination of the period of the solutions. The method is applied to the linear harmonic oscillator, a couple of nonlinear oscillators, the elastic pendulum and the Henon-Heiles system. The approach is used to trace the bifurcations of the periodic solutions of the last two, being 2 degree-of-freedom systems demonstrating very rich dynamical behavior. In the process, the advantages offered by the current formulation of the energy balance is brought out. A harmonic perturbation approach is used to evaluate the stability of the solutions for the bifurcation diagram. [ABSTRACT FROM AUTHOR]

Passive acoustic liners, used in aeronautic engine nacelles to reduce radiated fan noise, have a quarter-wavelength behavior, because of perforated sheets backed by honeycombs (with one or two degrees of freedom). However, their acoustic absorption ability is naturally limited to medium and high frequencies because of constraints in thickness. The low ratio “plate thickness/hole diameter” generates impedance levels dependent on the incident sound pressure level and the grazing mean flow (by a mechanism of nonlinear dissipation through vortex shedding), which penalises the optimal design of liners. The aim of this paper is to overcome this problem by a concept called LEONAR (“Long Elastic Open Neck Acoustic Resonator”), in which a perforated plate is coupled with tubes of variable lengths inserted in a limited volume of a back cavity. To do this, experimental and theoretical studies, using different types of liners (material nature, hole diameter, tube length, cavity thickness) are described in this paper. It is shown that the impedance can be precisely determined with an analytical approach based on parallel transfer matrices of tubes coupled to the cavity. Moreover, the introduction of tubes in a cavity of a conventional resonator generates a significant shift in the frequency range of absorption towards lower frequencies or allows a reduction of cavity thickness. The impedance is practically independent of sound pressure level because of a high ratio “tube length/tube hole diameter”. Finally, a test led in an aeroacoustic bench suggests that a grazing flow at a bulk Mach number of 0.3 has little impact on the impedance value. These first results allow considering these resonators with linear behavior as an alternative to classical resonators, in particular, as needed for future Ultra High Bypass Ratio engines with shorter and thinner nacelles. [ABSTRACT FROM AUTHOR]