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The work herein proposes the use of the data-driven Loewner-framework for reduced order modeling as applied to dynamic Finite Element Models (FEM) of thermally morphing structures. The Loewner-based modeling approach is computationally efficient and accurately constructs reduced models using analytical output data from a FEM. This paper details the two-step process proposed in the Loewner approach. First, a random vibration FEM simulation is used as the input for the development of a Single Input Single Output (SISO) data-based dynamic Loewner state space model. Second, an SVD-based truncation is used on the Loewner state space model, such that the minimal, dynamically representative, state space model is achieved. For this second part, varying levels of reduction are generated and compared. The work herein can be extended to model generation using experimental measurements by replacing the FEM output data in the first step and following the same procedure. This method will be demonstrated on two thermally morphing structures, a rigidly fixed hexapod in multiple geometric configurations and a low mass anisotropic morphing boom. This paper is working to detail the method and identify the benefits of the reduced model methodology. [ABSTRACT FROM AUTHOR]

Abstract Conventionally, the dynamic modeling of H-type gantry stage(HGS) assumes that the stiffness of mid-beam is extremely high so that its deformation is ignorable. This assumption apparently simplifies the study, but unavoidably compromises the modeling precision as it is not consistent with the real working status especially at high frequency motion. Comparing with similar studies on moving mass problems, the beam vibration of HGS is excited not only by the moving mass and system acceleration but also by the non-synchronized motion of the two moving ends of mid-beam. Therefore, the objective of this paper is to propose an assumed mode method based on simplified mode shapes(AMM-SMS) by simultaneously considering the lateral flexibility and the motion of the ends of mid-beam. The proposed AMM-SMS adopts the mode shapes of a simplified system, which has the same geometry boundary condition(BC) with the investigated system, to discretize the nonlinear kinematic equations of the proposed system. This method improves the modeling precision with low complexity, and can be applied in different BCs of FHGS. The proposed method is verified by various comparisons with the finite element method. Based on the AMM-SMS, the first three natural frequencies and mode shapes are studied. The open-loop responses of the system are obtained to analyze the effects of different BCs, of the motion of end-effector and of the external exciting force on the vibratory behavior. [ABSTRACT FROM AUTHOR]

Understanding thermal effects on the vibration of local (cable-dominant) modes in multi-cable structures is a complicated task. The main difficulty lies in the modification by temperature change of cable tensions, which are then undetermined. This paper applies a finite element procedure to investigate the effects of thermal loads on the linear dynamics of prestressed self-weighted multi-cable structures. Provided that boundary conditions are carefully handled, the discretization of cables with nonlinear curved beam elements can properly represent the thermoelastic behavior of cables as well as their linearized dynamics. A three-step procedure that aims to replace applied pretension forces with displacement continuity conditions is used. Despite an increase in the computational cost related to beam rotational degrees of freedom, such an approach has several advantages. Nonlinear beam finite elements are usually available in commercial codes. The overall method follows a thermoelastic geometrically non-linear analysis and hereby includes the main sources of non-linearities in multi-cable structures. The effects of cable bending stiffness, which can be significant, are also naturally accounted for. The accuracy of the numerical approach is assessed thanks to an analytical model for the vibration of a single inclined cable under temperature change. Then, the effects of thermal loads are investigated for two cable bridges, highlighting how natural frequencies can be affected by temperature. Although counterintuitive, a reverse relative change of natural frequency may occur for certain local modes. This phenomenon can be explained by two distinct mechanisms, one related to the physics intrinsic to cables and the other related to the thermal deflection of the superstructure. Numerical results show that cables cannot be isolated from the rest of the structure and the importance of modeling the whole structure for a quantitative analysis of temperature effects on the dynamics of cable bridges. [ABSTRACT FROM AUTHOR]

Abstract: FE model updating techniques are used to update dynamic FE models of structures in the light of modal test data. Iterative methods of model updating that update a set of chosen parameters of the model, so as to reduce the difference between the natural frequencies and the mode shapes of the FE model and the corresponding quantities obtained through a modal test on the structure, are probably the most widely used methods. Once experimental modal data has been identified, a necessary prior step, before updating can be carried out, is that of establishing the correspondence between the FE model modes and the experimentally identified modes. It is however experienced that, many a times a situation is encountered where not all of the modes identified through an experiment can be correlated with certainty with those predicted by the FE model and some experimental modes may be left uncorrelated. There could be several reasons for this lack of correlation as identified in the paper. But the consequence is that such uncorrelated modes cannot be used in FE model updating using existing iterative methods based on modal data even when they form valid known pieces of information about the structure. This is a disadvantage since it reduces the quantity of experimental data available for model updating and hence makes the updating process less effective in yielding an updated model that is a closer representation of the structure. This paper identifies this as a limitation of the existing iterative methods of model updating based on modal data and puts forward a notion of FE model updating using uncorrelated modes. The paper proposes a solution to overcome this limitation in the form of a new method of FE model updating that accepts both correlated as well as uncorrelated modes for updating. This is in contrast to all the current iterative modal data based methods of model updating that are based on the assumption of availability of correlated mode pairs and hence cannot use uncorrelated mode shapes and corresponding natural frequencies in the updating process. Formulation of the proposed method is described followed by a couple of numerical examples based on a beam structure to validate the method. The robustness of the method in the presence of simulated noise is also studied. Another numerical example of a more complex F-shape structure is also presented. The method is then validated though an experimental study. The proposed method is found to successfully update an FE model yielding correct estimates of the updating parameters in the presence of uncorrelated modes. [Copyright &y& Elsevier]

Abstract: In this paper, mode shapes of a cracked beam with a rectangular cross section beam are analysed using finite element method. The 3D beam element is applied for this finite element analysis. The influence of the coupling mechanism between horizontal bending and vertical bending vibrations due to the crack on the mode shapes is investigated. Due to the coupling mechanism the mode shapes of a beam change from plane curves to space curves. Thus, the existence of the crack can be detected based on the mode shapes: when the mode shapes are space curves there is a crack in the beam. Also, when there is a crack, the mode shapes have distortions or sharp changes at the crack position. Thus, the position of the crack can be determined as a position at which the mode shapes exhibit such distortions or sharp changes. While in previous studies using 2D beam element, distortions in the mode shapes caused by a small crack could not be detected, these distortions in the case using the 3D beam element can be amplified and inspected clearly by using the projections of the mode shapes on appropriate planes. The quantitative analysis is also implemented to relate the size and position of the crack with the observed coupled modes. These results can be applied for crack detection of a beam. In this paper, the stiffness matrix of a cracked element obtained from fracture mechanics is presented and numerical simulations of three case studies are provided. [Copyright &y& Elsevier]

Abstract: In this paper the closed form expression of the exact dynamic stiffness matrix of an Euler–Bernoulli beam in the presence of an arbitrary number of concentrated cracks is derived. The procedure adopted for the evaluation of the dynamic stiffness matrix is based on the availability of the exact closed form solution of the vibration modes of the multi-cracked beam, derived by the same authors in a previous paper. The knowledge of the exact explicit dynamic stiffness matrix of the multi-cracked beam makes the direct evaluation of the exact global dynamic stiffness matrix of damaged frame structures possible. Furthermore, it allows the exact evaluation of the frequencies and the corresponding vibration modes, consistent with the distributed parameter model, through the application of the well-known Wittrick–Williams algorithm. Some numerical applications, relative to the evaluation of frequencies and the corresponding mode shapes of multi-cracked framed structure, are reported. Furthermore, the closed-form solution has been validated by comparing with some exact results available in the literature, for a simple single cracked frame. Finally, further new results for a multi-cracked frame have been compared with those obtained by a finite element simulation. [Copyright &y& Elsevier]

An imprecise probability approach based on evidence theory is proposed for squeal instability analysis of uncertain disc brakes in this paper. First, the squeal instability of the finite element (FE) model of a disc brake is investigated and its dominant unstable eigenvalue is detected by running two typical numerical simulations, i.e., complex eigenvalue analysis (CEA) and transient dynamical analysis. Next, the uncertainty mainly caused by contact and friction is taken into account and some key parameters of the brake are described as uncertain parameters. All these uncertain parameters are usually involved with imprecise data such as incomplete information and conflict information. Finally, a squeal instability analysis model considering imprecise uncertainty is established by integrating evidence theory, Taylor expansion, subinterval analysis and surrogate model. In the proposed analysis model, the uncertain parameters with imprecise data are treated as evidence variables, and the belief measure and plausibility measure are employed to evaluate system squeal instability. The effectiveness of the proposed approach is demonstrated by numerical examples and some interesting observations and conclusions are summarized from the analyses and discussions. The proposed approach is generally limited to the squeal problems without too many investigated parameters. It can be considered as a potential method for squeal instability analysis, which will act as the first step to reduce squeal noise of uncertain brakes with imprecise information. [ABSTRACT FROM AUTHOR]

Optimal sensor placement technique plays a key role in structural health monitoring of spatial lattice structures. This paper considers the problem of locating sensors on a spatial lattice structure with the aim of maximizing the data information so that structural dynamic behavior can be fully characterized. Based on the criterion of optimal sensor placement for modal test, an improved genetic algorithm is introduced to find the optimal placement of sensors. The modal strain energy (MSE) and the modal assurance criterion (MAC) have been taken as the fitness function, respectively, so that three placement designs were produced. The decimal two-dimension array coding method instead of binary coding method is proposed to code the solution. Forced mutation operator is introduced when the identical genes appear via the crossover procedure. A computational simulation of a 12-bay plain truss model has been implemented to demonstrate the feasibility of the three optimal algorithms above. The obtained optimal sensor placements using the improved genetic algorithm are compared with those gained by exiting genetic algorithm using the binary coding method. Further the comparison criterion based on the mean square error between the finite element method (FEM) mode shapes and the Guyan expansion mode shapes identified by data-driven stochastic subspace identification (SSI-DATA) method are employed to demonstrate the advantage of the different fitness function. The results showed that some innovations in genetic algorithm proposed in this paper can enlarge the genes storage and improve the convergence of the algorithm. More importantly, the three optimal sensor placement methods can all provide the reliable results and identify the vibration characteristics of the 12-bay plain truss model accurately. [Copyright &y& Elsevier]

The aim of the paper is the evaluation and the prediction of the perceived quality of engine sounds, which is predicted in the design process by numerical simulations. Periodic combustion sounds of the operating engine are synthesized with the help of an overall numerical simulation approach before a real prototype exists. The perceived quality of the sound is rated in hearing tests using the method of relative comparison and absolute judgment. Results are transferred into an interval scaled ranking of the stimuli. Based on the data, a psychoacoustic model for sound quality is developed using psychoacoustic parameters. Predictions of this model are used to evaluate the sound quality of several technical design modifications, for example, different engine encapsulations. The results are visualized to allow a simple qualitative analysis of the sound perception. This results in an impartial and objective decision regarding the final design of an acoustic encapsulation with a higher perceived sound quality. [ABSTRACT FROM AUTHOR]

Abstract: The validity domain of Energy Finite Element Analysis (EFEA) is studied in this paper. The validity region and criterion of EFEA are studied theoretically from the formation of reverberant plane wave field, one of the main assumptions of EFEA. The studies are acquired by virtue of the equation of radiative energy transfer method, a similar wave method that can express the direct field and its conversion relationship with reverberant field exactly. The result shows that the SEA criterion of diffuse field derived by Le Bot can be used as a good indicator for the EFEA validity. Numerical simulations on a rectangular plate with different physical parameters are applied to validate the criterion. The validity region and the diagrams of validity of EFEA are assessed and discussed. Some noteworthy conclusions about EFEA are drawn. [Copyright &y& Elsevier]

Abstract: The paper is concerned with the analysis of dynamic behavior of elastic cylindrical shells of rotation subjected to an annular flow of compressible fluid (gas) having both the axial and tangential velocity components. The behavior of the rotating and flowing fluid is described in the framework of the potential theory. The elastic shell is considered based on the model of the classical shell theory. Numerical simulation is done using a semi-analytical variant of the finite element method. The results of numerical experiments made to analyze the stability of shells with different boundary conditions, geometrical dimensions and widths of the annular gap are discussed. The influence of the fluid rotation on the critical flow velocities and the influence of the axial flow on the critical angular velocities of fluid rotation are estimated with reference to the variants, in which one of the velocity components is not taken into account. The effect of elasticity of the outer shell on the boundary of hydroelastic stability is analyzed. [Copyright &y& Elsevier]

Abstract: The paper deals with the numerical simulation of the acoustic field in two-dimensional cavities in which absorbing materials are present. Though Finite Element Method (FEM) could be employed for this purpose, the discretization level required for achieving reasonable accuracy renders the method impractical in the mid-frequency range. To alleviate this limitation, the Partition of Unity Finite Element Method (PUFEM) using plane wave functions has been shown to be very effective for solving short wave Helmholtz problems. In the present work, the method is extended to the computation of the pressure wave field within the absorbing media which is modeled as a bulk-reacting material characterized by a complex-valued and frequency dependent mean density and dynamic compressibility. Lagrange multipliers are used to enforce the transmission conditions at the air–material interface. Performances of the PUFEM are compared with a standard FEM in several examples of practical interests. It is shown that the technique is a good candidate for solving noise control problems at high frequency. [Copyright &y& Elsevier]

Abstract: The vibration problems associated with geared systems have been the focus of research in recent years. As the torque is mainly transmitted by the geared system, a slant crack is more likely to appear on the gear shaft. Due to the slant crack and its breathing mechanism, the dynamic behavior of cracked geared system would differ distinctly with that of uncracked system. Relatively less work is reported on slant crack in the geared rotor system during the past research. Thus, the dynamic analysis of a geared rotor-bearing system with a breathing slant crack is performed in the paper. The finite element model of a geared rotor with slant crack is presented. Based on fracture mechanics, the flexibility matrix for the slant crack is derived that accounts for the additional stress intensity factors. Three methods for whirling analysis, parametric instability analysis and steady-state response analysis are introduced. Then, by taking a widely used one-stage geared rotor-bearing system as an example, the whirling frequencies of the equivalent time-invariant system, two types of instability regions and steady-state response under the excitations of unbalance forces and tooth transmission errors, are computed numerically. The effects of crack depth, position and type (transverse or slant) on the system dynamic behaviors are considered in the discussion. The comparative study with slant cracked geared rotor is carried out to explore distinctive features in their modal, parametric instability and frequency response behaviors. [Copyright &y& Elsevier]

Abstract: A finite-element algorithm is proposed to investigate the dynamic behavior of elastic shells of revolution containing a quiescent or a flowing inviscid fluid in the framework of linear theory. The fluid behavior is described using the perturbed velocity potential. The shell behavior is treated in the framework of the classical shell theory and variational principle of virtual displacements incorporating a linearized Bernoulli equation for calculation of hydrodynamic pressure acting on the shell. The problem reduces to evaluation and analysis of the eigenvalues in the connected system of equations obtained by coupling the equations for velocity perturbations with the equations for shell displacements. For cylindrical shells, the results of numerical simulations are compared with recently published experimental, analytical and numerical data. The paper also reports the results of studying the dynamic behavior of shells under various boundary conditions for the perturbed velocity potential. The investigation made for conical shells has shown that under certain conditions an increase in the cone angle can change a divergent type of instability to a flutter type. [Copyright &y& Elsevier]

Abstract: In this paper, sound transmission through an aircraft sidewall representative double panel structure is investigated theoretically and parametric and validation studies are conducted. The studied configuration is composed of a trim panel (receiver side panel) attached to a ribbed skin panel (source side panel) with periodically spaced resilient mounts. The structure is considered infinite in order to use space harmonic expansion. The partition is also assumed planar for simplicity. The model allows for a 3D incident field and the panels can be metallic and/or composite. A four-pole formulation is employed for modeling of the mounts and the absorption provided by the fiberglass that fills the cavity between the leaves is addressed with an equivalent fluid model. The investigation of mount stiffness, damping and spacing show that properly designed mounts can increase the TL significantly (up to 20dB of difference between rigid and resilient mounts). However, they can create undesirable resonances resulting from their interaction with the panels. The influence of cavity absorption is also studied and results illustrate the fact that it is not worth investing in a highly absorbent fiber if the structure-borne transmission path is not adequately insulated, and likewise that it is not worth investing in highly resilient mounts without sufficient cavity absorption. Moreover, the investigation of panel damping confirms that when structure-borne transmission is present, raising skin damping can increase the TL even below coincidence, but that on average, greater improvements are achieved by raising trim damping. Finally, comparison between the periodic model and finite element simulations for structure-borne transmission shows that the average level of transmitted energy is well reproduced with the periodic approach. However, the modes are only captured approximately due to the assumption of an infinite structure. [Copyright &y& Elsevier]

Abstract: This paper deals with local damages identification for strongly and weakly coupled beam systems with close and repeated natural frequencies based on the measured dynamic responses of the systems under external moving forces. The dynamic responses of the coupled beam systems are calculated from Newmark integration method and they are used for structural damage detection. The mode localization phenomenon due to local damage(s) in the weakly coupled beam system is studied. In the inverse analysis, a dynamic response sensitivity-based finite element model updating method is employed for the detection of local damage(s) in the coupled beam systems. Numerical simulation shows that the proposed method is effective in identifying the damages in the coupled beam systems with good accuracy from several measurements. It is found the proposed method is insensitive to artificial measurement noise and has the potential for practical applications. [Copyright &y& Elsevier]

Most of finite element model updating techniques do not employ damping matrices and hence, cannot be used for accurate prediction of complex frequency response functions (FRFs). In this paper, damped finite element model updating procedure is proposed and tested with the objective that the damped finite element updated model is able to predict the measured FRFs accurately. The proposed damped updating procedure is a two-step procedure. In the first step, mass and stiffness matrices are updated using FRF data and in the second step, damping matrix is identified using updated mass and stiffness matrices that are obtained in the previous step. The effectiveness of the proposed procedure is demonstrated by numerical examples as well as by actual experimental data. Firstly, a study is performed using a numerical simulation based on fixed¿fixed beam structure with non-proportional viscous damping model. The numerical study is followed by case involving actual measured data for the case of F-shaped test structure. The results have shown that the proposed procedure can be used for accurate prediction of the complex FRFs. [Copyright &y& Elsevier]

This paper investigates the dynamic response of a rotating multi-span shaft with general boundary conditions subjected to an axially moving load. The system equations of motion are derived based on the global assumed mode method and a modified transformation matrix is proposed to deal with the multi-span geometric constraints. The numerical results are solved by the Runge–Kutta method. To ensure the validity of the method, the convergence test for dynamic response and the comparison of natural frequencies obtained by both the present method and finite element method are demonstrated. Numerical simulations are performed to study the effects of the moving speed of the load, the number of spans, and the rotational speed of the shaft on the deflections under the moving load. In addition, the effects on the occurring position of maximum deflection are presented. The numerical results show that the maximum deflection in the direction of the load may occur at any span and near the midpoint of one span. However, the maximum deflection induced by the gyroscopic effect in the direction perpendicular to the load always occurs at the first span. Moreover, the occurring position of maximum deflection is independent of the rotational speed. [Copyright &y& Elsevier]

Abstract: In this study, two different dynamic models, a finite elements-based deformable-body model and a simplified discrete model, and a surface wear model are combined to study the interaction between gear surface wear and gear dynamic response. The proposed dynamic gear wear model includes the influence of worn surface profiles on dynamic tooth forces and transmission error as well as the influence of dynamic tooth forces on wear profiles. This paper first introduces the nonlinear dynamic models that include gear backlash and time-varying gear mesh stiffness, and a wear model separately. It presents a comparison to experiments for validation of the dynamic models. The dynamic models are combined with the wear model to study the interaction of surface wear and dynamic behavior in both linear and nonlinear response regimes. At the end, several sets of simulation results are used to demonstrate the two-way relationship between nonlinear gear dynamics and surface wear. [Copyright &y& Elsevier]

• A dual rotor experimental rig of an aero-engine is designed and manufactured. • Nonlinear dynamic model of the test rig is established based on finite element method. • Reduced-order model of dual rotor-bearing system is obtained by CMS method. • Local blade-casing rubbing fault feature is revealed by numerical simulation and experiments. In order to reveal the nonlinear vibration characteristics of an actual dual-rotor-aero-engine with blade-casing rubbing, a dual-rotor-bearing-coupling misalignment system with blade-casing rubbing are investigated based on numerical simulation and experimental measurement in this paper. A dual-rotor experimental rig is designed and manufactured, that is a simplified structure according a dual-rotor-aero-engine. The dynamic model of the dual- rotor-bearing system of the test rig is established based on the finite element method (FEM) taking into account the coupling misalignment, blade-casing rubbing and the nonlinearities of all of the supporting rolling element bearings. The component mode synthesis (CMS) method is applied to the model order reduction of the high-degrees of freedom (DOFs) dynamic model. The numerical and experimental nonlinear vibration responses of the dual-rotor system are compared with each other at different rotational speeds at different rotational speed ratios. The numerical results are in agreement with the experiment. These results reveal the nonlinear vibration characteristics of the dual-rotor-bearing-coupling misalignment system with local blade-casing rubbing fault. [ABSTRACT FROM AUTHOR]