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Fatigue Damage Spectra (FDS) and Extreme Response Spectra (ERS) are well-established tools for characterizing and evaluating the impact of vibration loads on mechanical structures. While this is particularly valuable in producing test-tailored specifications, their current application is limited to uniaxial analysis despite evidence indicating their inadequacy in representing real-world loads, which are often multiaxial. The proposed method offers a system-oriented approach to characterize and compare multiaxial environments in terms of their severity, independently or not of any physical structure. In addition, it introduces a generalization of the FDS and ERS, referred to as Fatigue Damage multi-Spectrum (FDmS) and Extreme Response multi-Spectrum (ERmS) respectively. These extensions allows for the consideration of multiaxial phenomena, such as correlation and modal proximity. Finally, this paper demonstrates through several case studies the method's capability to capture phenomena not addressed by established uniaxial approaches. [ABSTRACT FROM AUTHOR]

• This paper proposes a particle damping equivalent method based on force chain for simulating the behavior of PD. • The newly proposed method considers the contact between particles and the motion state of particles. • The shaking table test and corresponding numerical simulation are conducted under high-frequency vibration condition. • The effectiveness and superiority of the method are demonstrated and the particle motion state is confirmed. A particle damping equivalent method based on force chain is newly proposed for simulating the behavior of particle damper (PD) with higher accuracy. Compared with other existing equivalent methods, this method considers the contact between particles and evaluates the particle motion state. Firstly, the particle damping equivalent method based on the theory of force chain and contact model is proposed, and the simulation process of the equivalent method is described. Then, this equivalent method is adopted to simulate the high frequency vibration of pipe installed with PD using SAP2000 software. The simulated vibration response exhibits excellent agreement with experimental results, validating the effectiveness of the proposed equivalent method. Finally, based on the calculation results, it is observed that the particle motion state of the PD in the experiment is quasi-static. This further shows that the particle chain in the damper under high frequency vibration can ignore the wave propagation behavior, which aligns with the assumption of the particle contact model. [ABSTRACT FROM AUTHOR]

The quasi-Zero Stiffness (QZS) isolation system is a typical nonlinear isolation system, which has high static stiffness characteristics to improve the bearing capacity and deformation resistance, and its low dynamic stiffness characteristics can reduce the inherent frequency of the system to realize a wider vibration isolation frequency band, so it has a more excellent low-frequency vibration isolation performance compared with the linear system. In this paper, a horizontal QZS isolator is constructed based on a pre-compressed oblique spring system, and two sets of the horizontal QZS isolators are mechanically assembled to work together to achieve a bi-directional horizontal QZS isolation system. Considering that the construction of two sets of horizontal vibration isolators is approximately the same, we focus on one of the isolators for the static analysis and derive the parameter conditions to be satisfied for achieving quasi-zero stiffness characteristics. We considered the effect of each adjustable parameter of the horizontal vibration isolator on the mechanical performance of the QZS system, and sought to optimize the QZS interval to improve the vibration isolation performance. A comparative study of the dynamical properties between the QZS system with ordinary and optimized parameters, as well as the equivalent linear system, is further carried out by means of nonlinear approximate analysis. Finally, the dynamic characteristics of the bi-directional horizontal QZS system and the equivalent linear system are compared by shaker tests on the prototype device, which proved the excellent vibration isolation performance of the proposed QZS isolation system. [ABSTRACT FROM AUTHOR]

Abstract This paper is concerned with the free vibration problem of multiply connected bar-chain (MCB) system with direct and indirect neighbouring interactions. MCB is a line of rigid bars connected by multiple elastic rotational springs. The so-called direct or indirect neighbouring interactions are realized by connections between two adjacent bars or two distant bars by the rotational springs. The free vibration frequencies of two-neighbouring interacted and p -neighbouring interacted MCB are analytically obtained for simply supported end restraints. A nonlocal continuum model is built based on this lattice model by continualizing the discrete equations. This continualized nonlocal model (CNM) is found to be equivalent to the Eringen's stress gradient nonlocal model. The expression of the length scale of CNM is figured out and it is found to be dependent on the rotational spring stiffnesses of MCB. Exact nonlocal vibration frequencies are predicted with the calibrated length scale. The comparison between CNM and MCB shows that the scale effect of a generalized lattice system including multiple interactions could be captured by the simple nonlocal continuum model. [ABSTRACT FROM AUTHOR]

In this paper, for the first time, by applying molecular dynamics simulation in conjugation with frequency domain decomposition, it was demonstrated that borophene resonators are at least 100% more efficient than graphene ones. It was also shown that this significant superiority does not arise solely from the difference between the molecular weights of borophene and graphene, but rather from the amazing intrinsic mechanical properties of borophene. Interest in detecting lower masses and lower pressures has led to a scientific race to find resonators with higher resonant frequencies. As a powerful rival of graphene, and used to fabricate sensors with lower-than-zeptogram resolutions, borophene promises enhanced future capabilities. Studies of the effects of geometrical parameters have verified that resonance is fully dependent on resonator size and chirality. The fundamental natural frequency of a rectangular borophene sheet is much higher when its zigzag edge is longer than the armchair edge, but not the other way around. Generally, it can be concluded that a rectangular borophene resonator with a longer zigzag edge achieves a higher resonance than a graphene resonator of equivalent weight. As a final fascinating conclusion: Borophene seems to be superior to graphene in resonance applications. [ABSTRACT FROM AUTHOR]

Abstract: In previous paper by the authors, the inner product vector (IPV) was proposed as a damage detection algorithm which uses cross correlation functions between vibration responses under band pass white noise excitation. As the characteristics of IPVs calculated by different vibration responses (i.e. displacement, velocity and acceleration) under band pass white noise excitation with different frequency range should be different, the effectiveness of the damage detection method may be affected by the response type and excitation frequency range. This paper just investigates the effect of response type and excitation frequency range on the IPV-based structural damage detection method. Firstly, the theoretical formulae of IPVs and the damage index using IPV are reviewed shortly. Then, the effect of response type on the IPVs is analyzed based on the characteristics of the theoretical formulae of IPVs, and the principle for choosing the response type for calculating IPV under band pass white noise excitation with different frequency range is proposed as well. Finally, simulative damage detection examples of a shear frame structure are presented to illustrate the theory and method proposed in this paper. [Copyright &y& Elsevier]

The speed fluctuation of satellite-rotary-mechanisms causes vibration of slightly different frequencies. The critical requirements of satellites need a vibration control device with high frequency resolution to suppress the vibration. This paper presents a coarse-fine adaptive tuned vibration absorber (ATVA) with high frequency resolution. The coarse-fine ATVA which simultaneously satisfies the requirements of high resolution and relatively wide effective bandwidth is capable of tracking the variable exciting frequency adaptively to suppress the vibration of the primary system. The coarse-fine ATVA is divided into a coarse tuning segment and a fine tuning segment. The coarse tuning segment is used to tune the required natural frequency in a relatively wide effective bandwidth and the fine tuning segment can achieve precise tune in a tiny-scale bandwidth. The mathematical model of the coarse tuning and the fine tuning is proposed to design the parameters of the coarse-fine ATVA. The experimental test results indicate the coarse tuning bandwidth of the coarse-fine ATVA is 8.7 Hz to 29 Hz and the minimum resolution of the fine tuning is 0.05 Hz. Moreover, a significant vibration attenuation of 15dB is verified in the effective bandwidth. [ABSTRACT FROM AUTHOR]

In this paper, a new method and formulation is presented for experimental measurement of energy density of high frequency vibrations of a plate. By use of the new proposed method and eight accelerometers, both kinetic and potential energy densities are measured. Also, a computer program is developed based on energy finite element method to evaluate the proposed method. For several points, the results of the developed experimental formulation are compared with those of the energy finite element analysis results. It is observed that, there is a good agreement between experimental results and analyses. Finally, another test setup with reduced accelerometer spacing was prepared and based on the comparison between kinetic and potential results, it is concluded that, the kinetic and potential counterparts of the energy density are equal in high frequency bands. Based on this conclusion, the measurement procedure was upgraded to an efficient and very simple one for high frequency ranges. According to the new test procedure, another experimental measurement was performed and the results had a good agreement with the EFEA results. [ABSTRACT FROM AUTHOR]

Abstract: This paper presents a control strategy for the suppression of vibration due to unknown disturbance forces in large, nonlinear flexible structures. The control action proposed, based on the modal approach, consists of two contributions. The first is the well-known Independent Modal-Space Control, which increases system damping and improves its behavior close to the resonance frequencies. The second is a disturbance estimator, which calculates the modal components of the external forces acting on the system and compensates for them using actuator forces. The system modal coordinates, required by both logics, are estimated through a modal state observer. The proposed control logic is tested on a flexible boom. The paper reports the numerical and experimental results both for the linear and nonlinear (large motion) boom configuration. [Copyright &y& Elsevier]

Abstract: This paper presents an experimental study of the nonlinear dynamic characteristics of taut steel cables using a 3-D motion analysis system. In the experiment, the taut cables have one end fixed and the other end subject to harmonic vertical excitation. The 3-D motion analysis system can simultaneously record (with high resolution) the instant 3-D coordinates of the multiple markers fixed on a vibrating cable; this distinguishes it from other experimental systems used in vibration studies, in which the vibration of only one single point can be recorded during each individual testing. With the 3-D motion analysis system, this experimental study presents a distinctive interpretation of the dynamic characteristics of taut cables in spatial domain (based on the mode-shape information of the entire cable), in addition to one in time domain (based on real-time traces of one single point). This paper introduces the 3-D motion analysis system and experimental setup, discusses practical experimental procedures, and presents a detailed analysis of three sets of experimental vibration data of three taut steel cables with different small sags. The frequency response curves were obtained for three cables. For one of the three taut cables, more informative vibration data were recorded; this cable was studied in greater detail via modal analysis using a modal decomposition technique and nonlinear time-series analysis. [Copyright &y& Elsevier]

Abstract: Over the past three decades, a wide variety of active control methods have been proposed for controlling problematic vibration. The vast majority of approaches make the implicit assumption that sensors or actuators can be located in the region where vibration attenuation is required. However this is either not feasible or prohibitively expensive for many large scale structures or where the system environment is harsh. As a result, optimal control of local vibration may lead to enhancement at remote locations. Controlling remote vibration using only local sensing and actuation is an important concept to resolve this remote vibration control problem. Recently, a geometric methodology that provides an approach for defining the design freedom available for reducing vibrations at both local and remote locations has been proposed by the authors. In an earlier paper, the fundamental results were used to develop design procedures for discrete frequency control; in the current paper, however, the focus is on design procedures for broad band control. A systematic approach is developed that provides an additional design constraint to the geometric methodology to ensure that the resulting compensator provides closed loop stability. The design procedure is illustrated through its application to an active vibration isolation structure. [Copyright &y& Elsevier]

Abstract: In this paper an initial boundary value problem for a linear equation describing an axially moving stretched beam will be considered. The velocity of the beam is assumed to be time varying. Since the order of magnitude of the bending stiffness terms depends on the vibration modes and the frequencies involved a combination of two simplified models (that is, a string equation for the lower frequencies and a beam with string effect equation for the higher frequencies) will be used to describe the transversal vibrations of the system accurately. Based on the calculations of the natural frequencies the regions of applicability of these sub-models will be determined. A two time-scales perturbation method will be used to construct formal asymptotic approximations of the solutions. Non-resonant and some resonant cases will be studied for four different values of the relative errors. An important implication of the earlier results in the literature is that for these types of axially moving continua problems the use of only string-like models is not appropriate. To describe the dynamics of these types of axially moving continua problems correctly one has to include (small) bending stiffness in the model. In this paper it is explicitly shown how to work with a combined model that is a string model at the low frequencies and a tensioned beam model at the higher frequencies. [Copyright &y& Elsevier]

Abstract: In this paper, an energy-density field approach applied to the vibroacoustic analysis of complex industrial structures in the low- and medium-frequency ranges is presented. This approach uses a statistical computational model. The analyzed system consists of an automotive vehicle structure coupled with its internal acoustic cavity. The objective of this paper is to make use of the statistical properties of the frequency response functions of the vibroacoustic system observed from previous experimental and numerical work. The frequency response functions are expressed in terms of a dimensionless matrix which is estimated using the proposed energy approach. Using this dimensionless matrix, a simplified vibroacoustic model is proposed. [Copyright &y& Elsevier]

Abstract: The aim of this paper is to show that the image source method (ISM) can be used both for analytically calculating Green''s functions of particular simply supported convex polygonal plates and for predicting medium and high frequency vibrations of arbitrarily shaped simply supported convex polygonal plates with controllable precision. In the first part of the paper, the method for obtaining the Green''s function of a polygonal plate by ISM is developed. Examples for plates of different geometries (rectangle, isosceles right triangle, half-equilateral triangle and equilateral triangle) are given. In the second part of the paper, the pertinence of ISM for predicting medium and high frequency vibrations of arbitrarily shaped simply supported convex polygonal plates is investigated. An approximation based on the exclusion of image sources beyond a certain distance from the receiver is used in order to take advantage of the dissipation of vibrational energy through wave propagation. We investigate the influence of structural damping and truncation distance on the accuracy of such approximation. The computed responses are in good agreement with reference solutions, which are analytically known or obtained by the finite element method. [Copyright &y& Elsevier]

In this paper a new analytical method for solving the differential equations which describe the motion of the oscillator with fraction order elastic force is introduced. Using the first integral of motion the exact period of vibration in the form of the Euler beta function is obtained. Based on that value the approximate solution of the strong nonlinear fraction order differential equation is formed. The suggested procedure is applied for various fraction values, but also for the pure quadratic, cubic and quintic oscillators. The advantage of the suggested method is that is valid for all fraction values , the accuracy of the approximate solution is very high as the period of vibration is exactly analytically determined and is independent on the time. In the paper the fraction order differential equation with small linear and nonlinear terms is also considered. The Krylov–Bogolubov method is extended due to the fact that frequency of vibration depends on the amplitude of vibration. The approximate solution is with time variable amplitude, phase and frequency. The linear damped fraction order oscillator is widely discussed. The approximate solution of the differential equation which describes the vibrations of such oscillator is compared with exact numerical one and shows a good agreement. [Copyright &y& Elsevier]

Abstract: The concept of nonlinear normal modes (NNMs) is discussed in the present paper and its companion, Part II. Because there is virtually no application of the NNMs to large-scale engineering structures, these papers are an attempt to highlight several aspects that might drive their development in the future. Specifically, we support that (i) numerical methods for the continuation of periodic solutions pave the way for an effective and practical computation of NNMs, and (ii) time–frequency analysis is particularly suitable for the analysis of the resulting dynamics. Another objective of the present paper is to describe, in simple terms, and to illustrate the fundamental properties of NNMs. This is achieved to convince the structural dynamicist not necessarily acquainted with them that they are a useful framework for the analysis of nonlinear vibrating structures. [Copyright &y& Elsevier]

In the global framework of improving vibro-acoustic numerical simulations together with the need to decrease the number of prototyping stages, improving the quality for acoustic models becomes increasingly important for many industries such as automotive companies, for instance. This paper focuses on achieving greater accuracy for acoustic numerical simulations by making use of a parametric updating technique, which enables tuning the model parameters inside physically meaningful boundaries. The improved model is used for the next prototyping stages, allowing more accurate results within reduced simulation times. The updating technique used in this paper is based on recent works dealing with the constitutive relation error (CRE) method applied to acoustics. The updating process focuses on improving the acoustic damping matrix related to the absorbing properties of the materials covering the borders of the acoustic domain. The present study proposes a 2-stage optimization process, which exhibits many advantages. Indeed, the computational time decreases, the frequency interpolation of the material absorbing properties outside the studied frequency range is easily performed, and comparing the correlation of several material absorbing constitutive equations with experimental records is fast. Additional originality of the work comes with the application of the CRE updating method to a concrete real-life device, while previous works addressed purely numerical setups without experimental data. The test-case is the TRICARMO setup engineered by LMS International in Leuven, Belgium. The TRICARMO setup is a simplified car cabin with rigid walls and car seats inside. Thanks to the 2-stage approach, the material property characterization of the seat is improved by running the updating simulation process using a physical absorbing material model. [Copyright &y& Elsevier]

A gradient-based method for optimizing non-uniformly distributed multiple tuned mass damper (MTMD) is presented in this paper. By solving an optimization problem with multiple objectives, optimized non-uniformly distributed MTMDs are obtained. Then the dynamic characteristics, effectiveness, robustness and redundancy of MTMDs are investigated in detail. Without restrictive assumptions such as uniformly distributed frequency, identical damping ratio, the optimized non-uniformly MTMDs obtained here can be considered as the “true” optimal ones. Unlike the references [L. Zuo, S.A. Nayfeh, Optimization of the individual stiffness and damping parameters in multiple-tuned-mass–damper system, Journal of Vibration and Acoustics—Transactions of the ASME 127(1) (2005) 77–83; N. Hoang, P. Warnitchai, Design of multiple tuned mass damper by using a numerical optimizer, Earthquake Engineering and Structural Dynamics 34(2) (2005) 125–144], the maximum displacement or frequency response of the main structure is chosen as the objective function in the present paper, because the maximum displacement is more concerned than the root-mean-square response sometimes. Using the presented method, the errors of estimate of the parameters of the structure and the MTMD can be taken into account quantitatively in the design procedure of the MTMD. It is demonstrated that the MTMDs designed in this paper are more effective than the traditional optimal uniformly distributed MTMDs whose frequency spacing, stiffness or mass and damping are under some restrictions for simplicity. And the MTMDs designed by accounting for possible errors of estimate are more robust than those without consideration of errors. [Copyright &y& Elsevier]

The literature regarding the free vibration analysis of single-span beams carrying a number of spring–mass systems is plenty, but that of multi-span beams carrying multiple spring–mass systems is fewer. Thus, this paper aims at determining the “exact” solutions for the natural frequencies and mode shapes of a uniform multi-span beam carrying multiple spring–mass systems. Firstly, the coefficient matrices for an intermediate pinned support, an intermediate spring–mass system, left-end support and right-end support of a uniform beam are derived. Next, the numerical assembly technique for the conventional finite element method is used to establish the overall coefficient matrix for the whole vibrating system. Finally, equating the last overall coefficient matrix to zero one determines the natural frequencies of the vibrating system and substituting the corresponding values of integration constants into the related eigenfunctions one determines the associated mode shapes. In this paper, the natural frequencies and associated mode shapes of the vibrating system are obtained directly from the differential equation of motion of the continuous beam and no other assumptions are made, thus, the last solutions are the exact ones. The effects of attached spring–mass systems on the free vibration characteristics of the 1–4-span beams are studied. [Copyright &y& Elsevier]

Abstract: An adaptive mode superposition and acceleration technique (AMSAT) is proposed and implemented into the computation of frequency response functions (FRFs) and their sensitivities. Based on the mode superposition and mode acceleration methods for the FRFs, m-version, s-version, and ms-version adaptive schemes are presented. In these schemes, the error resulted from the mode truncation and/or series truncation is, at first, estimated at every specific frequency, respectively. Then, one more mode (called m-version), or one more level of the series (called s-version), or the combination (called ms-version) is included in the computation of the FRF when its error is greater than the error tolerance. The new FRF is recalculated and its error is re-evaluated. This procedure is repeated until all the errors fall below the specified value. Although only the implementation of FRFs and their sensitivities is demonstrated in this paper, the proposed adaptive technique may be applied to the computation of dynamic responses in time domain and their sensitivities, sensitivity of eigenpairs, modal energy, etc. One numerical example is included to demonstrate the application of the proposed adaptive schemes. The results show that the present schemes work very well. The s- and ms-version adaptive schemes are much more efficient than m-version scheme. Since the intention of this paper is to propose these new procedures, the damping, particularly the non-classical damping, is not included due to the complexity. [Copyright &y& Elsevier]

Abstract: This paper investigates the dynamic response of a class of electrostatically driven microelectromechanical (MEM) oscillators. The particular systems of interest are those which feature parametric excitation that arises from forces produced by fluctuating voltages applied across comb drives. These systems are known to exhibit a wide range of behaviors, some of which have escaped explanation or prediction. In this paper we examine a general governing equation of motion for these systems and use it to provide a complete description of the dynamic response and its dependence on the system parameters. The defining feature of this equation is that both the linear and cubic terms feature parametric excitation which, in comparison to the case of purely linear parametric excitation (e.g. the Mathieu equation), significantly complicates the system''s dynamics. One consequence is that an effective nonlinearity for the overall system cannot be defined. Instead, the system features separate effective nonlinearities for each branch of its nontrivial response. As such, it can exhibit not only hardening and softening nonlinearities, but also mixed nonlinearities, wherein the response branches in the system''s frequency response bend toward or away from one another near resonance. This paper includes some brief background information on the equation of motion under consideration, an outline of the analytical techniques used to reach the aforementioned results, stability results for the responses in question, a numerical example, explored using simulation, of a MEM oscillator which features this nonlinear behavior, and preliminary experimental results, taken from an actual MEM device, which show evidence of the analytically predicted behavior. Practical issues pertaining to the design of parametrically excited MEM devices are also considered. [Copyright &y& Elsevier]

Abstract: The vibration neutralizer has been used in many applications since invented. In many cases, an ingenious design law called fixed-points theory was utilized in determining the optimum tuning and damping ratios of the device. However, those applications are limited to point response control of a relatively simple structure. There are some applications related to continuous structures but the purpose is for point response control, collocated or non-collocated. In this paper, the fixed-points theory is examined for global vibration control namely the control of the kinetic energy of a continuous structure. It is proven in this paper that the same design law is applicable for a more complicated purpose. The results presented in this paper may offer new ways of using the device. [Copyright &y& Elsevier]

Abstract: In 1972 A. H. Vincent, the then Chief Dynamicist at Westland Helicopters, discovered that when a structure excited at point p with a constant frequency is modified, for example by the addition of a spring between two points r and s, then the response at another point q traces a circle when plotted in the complex plane as the spring stiffness is varied from minus infinity to plus infinity. This discovery, although apparently little known today, has many useful applications some of which are described in papers by various authors appearing in the 1970s and early 1980s. Vincent''s discovery is in fact a particular example of the bilinear transformation due to August Ferdinand Moebius (1790–1868). In this paper, the Vincent circle method is generalized for the case of any straight-line modification in the complex plane, typically , where . A new method for the visualization of Vincent circle results, including the case of multiple modifications is also presented. [Copyright &y& Elsevier]

In this paper the smooth function method, previously proposed for bending vibrations, is extended to the calculation of longitudinal natural frequencies of a vibrating isotropic bar with an arbitrary finite number of symmetric transverse open cracks. Moreover, the transfer matrix approach and the finite element method are considered to deal with the same problem. The paper includes several examples related to bars with three cracks which permit the comparison of natural frequencies predicted by these three methods. [Copyright &y& Elsevier]

Nonlinear energy harvesters are very sensitive to ambient vibrations. If the excitation level is too low, their large-amplitude oscillations for high-energy voltage output cannot be obtained. A nonlinear tristable energy harvester has been previously proposed to achieve more effective broadband energy harvesting for low-level excitations. However, the sensitivity of its dynamic characteristics to the system parameters remains uninvestigated. Therefore, this paper theoretically analyzes the influence of the external load, the external excitation, the internal system parameters and the equilibrium positions on the dynamic responses of nonlinear tristable energy harvesters by using the harmonic balance method. In addition, numerical acceleration excitation thresholds and basins of attraction are provided to investigate the potential for energy harvesting performance enhancement using the suitable equilibrium positions, appropriate initial conditions or external disturbances, due to high-energy interwell oscillations in the multi-solution ranges. More importantly, experimental voltage responses of a given tristable energy harvester versus the external excitation frequency and amplitude verify the existence of experimental multi-solution ranges and the effectiveness of the theoretical analysis. It is also revealed that achieving high-energy interwell oscillations in the multi-solution ranges of tristable energy harvesters will be feasible for improving energy harvesting from low-level ambient excitations. [ABSTRACT FROM AUTHOR]

Frequency response analysis requires the evaluation of an associated function for a typically large number of frequencies. Direct method for performing these calculations is time-consuming. In this paper, a method is proposed for solving frequency responses of a mechanical system with proportional damping. The method combines modal superposition with a model order reduction. Only the modes corresponding to a frequency range which is a little bigger than that of interest are used for modal superposition. Complementary part of contribution of computed modes for frequency response is calculated by a model order reduction method. Basis vectors are obtained by applying preconditioned conjugate gradient method to a modified undamped system at the highest frequency of interest. The existing factorized stiffness matrix developed for partial eigensolutions is used as preconditioner. This computational methodology is illustrated by its applications to two frequency response problems. It is shown that the present method can remarkably reduce the CPU time required by the direct method to frequency response analysis. [ABSTRACT FROM AUTHOR]

The classical problem for the application of a tuned vibration absorber is to minimize the response of a structural system, such as displacement, velocity, acceleration or to maximize the energy dissipated by tuned vibration absorber. The development of explicit optimal absorber parameters is challenging for a damped structural system since the fixed points no longer exist in the frequency response curve. This paper aims at deriving a set of simple design formula of tuned vibration absorber with nonlinear viscous damping based on the frequency tuning for harmonic load for a damped structural system under white noise excitation. The vibration absorbers being considered include tuned mass damper (TMD) and liquid column vibration absorber (LCVA). Simple approximate expression for the standard deviation velocity response of tuned vibration absorber for damped primary structure is also derived in this study to facilitate the estimation of the damping coefficient of TMD with nonlinear viscous damping and the head loss coefficient of LCVA. The derived results indicate that the higher the structural inherent damping the smaller the supplementary damping provided by a tuned vibration absorber. Furthermore, the optimal damping of tuned vibration absorber is shown to be independent of structural damping when it is tuned using the frequency tuning for harmonic load. Finally, the derived closed-form expressions are demonstrated to be capable of predicting the optimal parameters of tuned vibration absorbers with sufficient accuracy for preliminary design of tuned vibration absorbers with nonlinear viscous damping for a damped primary structure. [ABSTRACT FROM AUTHOR]

Abstract: In this paper, frequency measurement methods of resonant vibratory gyroscopes are studied. First, the working principle and dynamic output characteristics of the resonant vibratory gyroscope are introduced, which provide a theoretical analysis base to analyze the dynamic frequency output characteristic of the resonant vibratory gyroscope. Moreover, some relevant frequency measurement methods are introduced, a frequency measurement method based on dynamic output characteristics has been proposed for the purpose of investigating the modulated output signal of resonant vibratory gyroscopes. Finally, in order to verify the feasibility of the proposed frequency measurement method, resonator oscillator and dynamic frequency measurement experiments of the resonant vibratory gyroscopes are built. It is concluded from the resonator oscillator result that the designed and observed resonant frequency of the resonator have a good match, which shows the design of resonator oscillator is feasible. It is concluded from the dynamic frequency measurement result that correlation coefficient of output fitted curve is 99.95%, and the output characteristic of the gyroscope is linear frequency output, which shows the effectiveness of the proposed frequency measurement method. [Copyright &y& Elsevier]

Abstract: This paper concerns an investigation into the use of cubic nonlinearity in a vibration neutralizer to improve its effectiveness. It is assumed that the frequency of the harmonic excitation is well above the resonance frequency of the machine to which the neutralizer is attached, and that the machine acts as a simple mass. It is also assumed that the response of the system is predominantly at the harmonic excitation frequency of the machine. The harmonic balance method is used to analyze the system. It is shown how the nonlinearity has the effect of shifting the resonant peak to a higher frequency away from the tuned frequency of the neutralizer so that the device is robust to mistune. In a linear neutralizer this can only be achieved by adding mass to the neutralizer, so the nonlinearity has a similar effect to that of adding mass. Some characteristic features are highlighted, and the effects of the system parameters on the performance are discussed. It is shown that, for a particular combination of the system parameters, the effect of the nonlinearity is also to increase the bandwidth of the device compared to the linear neutralizer with similar mass and damping. Some approximate expressions are derived, which facilitate insight into the parameters which influence the dynamics of the system. The results are validated by some experimental work. [Copyright &y& Elsevier]

Abstract: This paper deals with the vibration characteristics of a piezoelectric open-shell transducer which was made by dividing a cylindrical piezoelectric transducer longitudinally into two segments. Two-dimensional governing equations were derived by using the cylindrical membrane theory. Applying mechanical and electrical boundary conditions yielded a characteristic equation for the resonance frequencies of the piezoelectric open-shell transducer. The fundamental frequency and the electromechanical coupling factor were calculated and compared with the results of the finite element analysis and experiment. The fundamental mode shape obtained theoretically was compared with the result of the finite element analysis. The theoretical analysis was verified to provide the vibration characteristics of an open-shell transducer. [Copyright &y& Elsevier]

Abstract: This paper designs and fabricates a vibration isolation model for improving vibration isolation effectiveness of the vehicle seat under low excitation frequencies. The feature of the proposed system is to use two symmetric negative stiffness structures (NSS) in parallel to a positive stiffness structure. Here, theoretical analysis of the proposed system is clearly presented. Then, the design procedure is derived so that the resonance peak of frequency–response curve drifts to the left, the load support capacity of the system is maintained, the total size of the system is reduced for easy practical application and especially, the bending of the frequency–response curve is minimized. Next the dynamic equation of the proposed system is set up. Then, the harmonic balance (HB) method is employed to seek the characteristic of the motion transmissibility of the proposed system at the steady state for each of the excitation frequency. From this characteristic, the curves of the motion transmission are predicted according to the various values of the configurative parameters of the system. Then, the time responses to the sinusoidal, multi frequency and random excitations are also investigated by simulation and experiment. In addition, the isolation performance comparison between the system with NSS and system without NSS is realized. The simulation results reveal that the proposed system has larger frequency region of isolation than that of the system without NSS. The experimental results confirm also that with a random excitation mainly spreading from 0.1 to 10Hz, the isolation performance of the system with NSS is greatly improved, where the RMS values of the mass displacement may be reduced to 67.2%, whereas the isolation performance of the system without NSS is bad. Besides, the stability of the steady-state response is also studied. Finally, some conclusions are given. [Copyright &y& Elsevier]

Abstract: This paper deals with the identification of a single open crack in a straight pipe containing fluid under pressure by frequency measurements. The crack is assumed to be a transverse partial cut of the pipe wall thickness with straight front and it is simulated by an equivalent elastic spring. It is shown that the measurement of the damage-induced shifts in a pair of natural frequencies of the bending vibration can be used to formulate and solve the diagnostic problem. In particular, it is shown that the change in the first two frequencies in a simply supported uniform pipe is sufficient to localize a small crack, except for a symmetrical position, and to determine the damage severity. Closed-form expressions are provided for damage location and severity. An extension of the method to simply supported uniform pipe with two cracks of equal severity is also presented. The analysis is based on an explicit expression of the frequency sensitivity to damage and allows to consider pipes under general set of boundary conditions. Analytical results agree well with the numerical tests. [Copyright &y& Elsevier]

Abstract: New developments in the simplified smearing technique for modeling vibrations of cross-stiffened, thin rectangular plates are presented. The computationally efficient smearing technique has been known for many years, but so far the accuracy of, say, predicted natural frequencies has been inadequate. The reason is that only the stiffeners at a right angle to the axis of angular motion are taken into account when calculating the bending stiffness, whereas the stiffeners that are parallel to this axis of angular motion are neglected. To improve predictions, the parallel stiffeners are taken into account in this paper. The improved smearing technique results in better accuracy for predicted natural frequencies of flat stiffened plates, as demonstrated for both simply supported and clamped boundary conditions. The improved prediction accuracy is demonstrated by comparing results from a numerical model based on the current development with results from finite element (FE) simulations that include the exact cross-sectional geometries of the stiffened panel. In order to demonstrate applications of the improved smearing technique, the predicted forced response is compared with both experimental and FE results. Another improvement concerns the orientation of the stiffeners. The original smearing technique presupposes that the stiffeners are parallel to the edges of the plate, but simple considerations make it possible to relax this requirement. To test the validity of the resulting technique a series of plates are examined for stiffeners angled relative to the plate edges. [Copyright &y& Elsevier]

Abstract: The paper presents an integrated vibration-based method for delaminations detection in homogeneous and composite beams. The method is based on Haar wavelets and artificial neural networks (ANNs). Firstly, scaled modal responses of the structure are expanded into Haar series by Chen–Hsiao method (CHM), and a delamination feature index is constructed. The database of 68 datasets built on Haar wavelet and frequency-based approaches was utilized by different ANNs to establish the mapping relationship between the delamination status and the delamination feature index or frequencies. The results are compared to each other. The simulations show the proposed complex method with delamination index detects the location of delaminations and identifies the delamination extent with high precision (); the approach requires less computations and processing time than the frequency-based approach. [Copyright &y& Elsevier]

Abstract: This paper addresses the issue of design of a passive vibration absorber in the presence of uncertainties in the forcing frequency. A minimax problem is formulated to determine the parameters of a vibration absorber which minimize the maximum motion of the primary mass over the domain of the forcing frequency. The limiting solutions corresponding to the forcing frequency being unrestricted and to that where the forcing frequency is known exactly, are shown to match those available in the literature. The transition of the optimal vibration absorber parameters between the extreme two cases is presented and the solutions are generalized by permitting the mass ratio of the absorber mass and the primary mass to be design parameters. For the specific case where the primary system is undamped, detailed analysis is presented to determine the transition of the optimal vibration absorber parameters between three distinct domains of solutions. [Copyright &y& Elsevier]

Abstract: A pneumatic suspension that can adapt itself to the incoming vibration is presented in this paper. A switching control strategy between two different configurations is proposed and studied. The objective is to avoid undesirable resonant frequencies. The control procedure is based on the pre-knowledge of the incoming vibration frequency, and when this frequency is unknown, a very efficient prediction technique is used. The results show that the adaptable suspension has improved performance as compared to any of its passive counterparts. The transient response when switching typically takes less than three cycles and does not hinder the suspension performance. [Copyright &y& Elsevier]

Abstract: The use of dynamic vibration absorbers to control the vibration of a structure in both narrow and broadbands is discussed in this paper. As a benchmark problem, a plate incorporating multiple vibration absorbers is formulated, leading to an analytical solution when the number of absorbers yields one. Using this analytical solution, control mechanisms of the vibration absorber in different frequency bandwidths are studied; the coupling properties due to the introduction of the absorber into the host structure are analyzed; and the control performance of the absorber in different control bandwidths is examined with respect to its damping and location. It is found that the interaction between the plate and the absorber by means of the reaction force from the absorber plays a dominant role in a narrow band control, while in a relatively broadband control the dissipation by the absorber damping governs the control performance. When control bandwidth further enlarges, the optimal locations of the absorbers are not only affected by the targeted mode, but also by the other plate modes. These locations need to be determined after establishing a trade-off between the targeted mode and other modes involved in the coupling. Finally, numerical findings are assessed based on a simply-supported plate and a fair agreement between the predicted and measured results is obtained. [Copyright &y& Elsevier]

Abstract: This paper presents experimental as well as analytic results on a rotational-pendulum vibration absorber. The characteristic frequencies of the absorber can be tuned dynamically by adjusting the rotational speed. The device is coupled to the primary structure through a mechanical spring, thus possessing two natural modes of vibrations in the vertical plane. When the primary structure is excited by a harmonic disturbance of which the frequency matches one of the two natural frequencies, the oscillations will be minimized. Whether the pendulum absorber is operating in a resonant mode can be detected by measuring the phase difference between the motions of the primary structure and the absorber, which provides an efficient way to tune the rotational speed for optimal performance. Experimental results confirm the theoretical developments and also demonstrate the effectiveness of the proposed scheme. [ABSTRACT FROM AUTHOR]

Abstract: In a recent work [Journal of Sound and Vibration 323 (2009) 849–863] the authors presented an energy-density field approach for the vibroacoustic analysis of complex structures in the low and medium frequency ranges. In this approach, a local vibroacoustic energy model as well as a simplification of this model were constructed. In this paper, firstly an extension of the previous theory is performed in order to include the case of general input forces and secondly, a structural partitioning methodology is presented along with a set of tools used for the construction of a partitioning. Finally, an application is presented for an automotive vehicle. [ABSTRACT FROM AUTHOR]

Abstract: This paper theoretically investigates the use of inertial actuators to reduce the sound radiated by a submarine hull in bending vibration under harmonic excitation from the propeller. The radial forces from the propeller are tonal at the blade passing frequency and are transmitted to the hull through the stern end cone. The hull is modelled as a fluid loaded cylindrical shell with ring stiffeners and two equally spaced bulkheads. The cylinder is closed by end-plates and conical end caps. The actuators are arranged in circumferential arrays and attached to the prow end cone. Both Active Vibration Control and Active Structural Acoustic Control are analysed. The inertial actuators can provide control forces with a magnitude large enough to reduce the sound radiated by the vibrations of the hull in some frequency ranges. [Copyright &y& Elsevier]

Abstract: This paper presents a novel device capable of generating three-dimensional vibrations with a single-axis of rotation. The device resembles a vibration motor with an eccentric weight, but the weight is allowed to move up and down in parallel to the axis of rotations. While spinning of the eccentric weight causes lateral vibrations, vertical vibrations are excited by superposing a periodic torque on the rotary shaft. The frequency and magnitude of vertical oscillations can be independently regulated. Since the vertical natural frequency is sensitive to rotational speeds, maximum vertical oscillations can be achieved by properly adjusting the rotational speed according to the excitation frequency. Relations between the excitation torque and the vertical shaking force are examined using the frequency response for the linearized system. Numerical simulations on the original nonlinear system are conducted to verify the performance of vertical oscillations. [Copyright &y& Elsevier]

Abstract: This paper aims at proposing an analytical model for the vibration analysis of horizontal beams that are self-weighted and thermally stressed. Geometrical nonlinearities are taken into account on the basis of large displacement and small rotation. Natural frequencies are obtained from a linearization of equilibrium equations. Thermal force and thermal bending moment are both included in the analysis. Torsional and axial springs are considered at beam ends, allowing various boundary conditions. A dimensionless analysis is performed leading to only four parameters, respectively, related to the self-weight, thermal force, thermal bending moment and torsional spring stiffness. It is shown that the proposed model can be efficiently used for cable problems with small sag-to-span ratios (typically , as in Irvine''s theory). For beam problems, the model is validated thanks to finite element solutions and a parametric study is conducted in order to highlight the combined effects of thermal loads and self-weight on natural frequencies. For cable problems, solutions are first compared with existing results in the literature obtained without thermal effects or bending stiffness. Good agreement is found. A parametric study combining the effects of sag-extensibility, thermal change and bending stiffness is finally given. [Copyright &y& Elsevier]

Abstract: This paper aims at investigating the effect of thermal stress on free linear vibrations of cables. An analytical model extending Irvine''s theory to thermoelasticity is proposed. In addition to the sag-extensibility parameter, this model yields a second dimensionless independent parameter related to the temperature change. Some general two-dimensional contour plots are presented giving the relative change in natural frequencies due to temperature with respect to the only two independent parameters of the problem. Depending on their values, this change can be quite significant. For in-plane symmetric modes, it is shown that a positive (resp. negative) temperature change does not necessarily decrease (resp. increase) natural frequencies and that thermoelastic effects can lead to cross-over due to the modification of the initial sag. [Copyright &y& Elsevier]

Abstract: The aim of this paper is to propose an effective method for extracting the beat characteristics and modal damping ratios of the bell type structures using the continuous wavelet transform (CWT). The bell type structures which can be simplified as a slightly asymmetric circular ring and cylindrical shell are commonly used to analyze those of a Korean bell. The beat response is caused by the mutual interference of mode pairs, which are created by the slight asymmetry of the bell type structures in the circumferential direction. First of all, the beat frequencies and periods of each vibration mode are obtained using the CWT based on the Gabor wavelet. Next, the modal damping ratios associated with the time duration of the beat response are also extracted by the CWT. When using the CWT on a given signal, the optimal shape of the Gabor wavelet used as the mother wavelet is determined by employing the Shannon entropy cost function on the normalized wavelet modulus. In order to show the accuracy of the proposed method, the beat characteristics and damping ratios are extracted from the simulated pure and noisy signals, which have mode pairs. Finally, the proposed method is applied to a small-sized Korean bell to verify its applicability in the field. [Copyright &y& Elsevier]

Abstract: The finite element and boundary element methods are employed in this study to investigate the sound radiation characteristics of a box-type structure. It has been shown [T.R. Lin, J. Pan, Vibration characteristics of a box-type structure, Journal of Vibration and Acoustics, Transactions of ASME 131 (2009) 031004-1–031004-9] that modes of natural vibration of a box-type structure can be classified into six groups according to the symmetry properties of the three panel pairs forming the box. In this paper, we demonstrate that such properties also reveal information about sound radiation effectiveness of each group of modes. The changes of radiation efficiencies and directivity patterns with the wavenumber ratio (the ratio between the acoustic and the plate bending wavenumbers) are examined for typical modes from each group. Similar characteristics of modal radiation efficiencies between a box structure and a corresponding simply supported panel are observed. The change of sound radiation patterns as a function of the wavenumber ratio is also illustrated. It is found that the sound radiation directivity of each box mode can be correlated to that of elementary sound sources (monopole, dipole, etc.) at frequencies well below the critical frequency of the plates of the box. The sound radiation pattern on the box surface also closely related to the vibration amplitude distribution of the box structure at frequencies above the critical frequency. In the medium frequency range, the radiated sound field is dominated by the edge vibration pattern of the box. The radiation efficiency of all box modes reaches a peak at frequencies above the critical frequency, and gradually approaches unity at higher frequencies. [Copyright &y& Elsevier]

Abstract: This paper deals with free vibration problems of uniform Timoshenko beams under various supporting boundary conditions. The technique we have used is based on applying the Adomian modified decomposition method (AMDM) to our vibration problems. Doing some simple mathematical operations on the method, we can obtain ith natural frequencies and mode shapes one at a time. The computed results agree well with those analytical and numerical results given in the literature. These results indicate that the present analysis is accurate, and provides a unified and systematic procedure which is simpler and more straightforward than the other modal analysis. [Copyright &y& Elsevier]

This study is the first work to consider the sound radiation of a panel subject to 2:1 internal resonance. The research also furthers the experimental work of a previous paper that did not make use of 2:1 internal resonance for sound reduction and failed to tune the frequency ratio of the first symmetric and anti-symmetric modes of the curved structure close to two. The results indicate that when the ratio of the resonant frequencies of the first bending symmetric and anti-symmetric modes is close to two, and the excitation frequency is equal to the resonant frequency of the first symmetric mode, the contribution of the first anti-symmetric mode is significant, even though the curved panel and excitation are symmetrical. This is because a large amount of the vibration energy is transferred to the anti-symmetric mode, whose sound radiation efficiency is much lower than that of the symmetric mode. Thus, the total sound radiated from the panel is reduced. [Copyright &y& Elsevier]

Nonlinear vibration of beams made of functionally graded materials (FGMs) containing an open edge crack is studied in this paper based on Timoshenko beam theory and von Kármán geometric nonlinearity. The cracked section is modeled by a massless elastic rotational spring. It is assumed that material properties follow exponential distributions through beam thickness. The Ritz method is employed to derive the governing eigenvalue equation which is then solved by a direct iterative method to obtain the nonlinear vibration frequencies of cracked FGM beams with different end supports. A detailed parametric study is conducted to study the influences of crack depth, crack location, material property gradient, slenderness ratio, and end supports on the nonlinear free vibration characteristics of cracked FGM beams. It is found that unlike isotropic homogeneous beams, both intact and cracked FGM beams show different vibration behavior at positive and negative amplitudes due to the presence of bending¿extension coupling in FGM beams. [Copyright &y& Elsevier]

One major drawback of the PolyMAX estimator, a polyreference least-squares frequency-domain estimator, is the lack of confidence bounds on the estimated modal parameters. This paper proposes a fast two-step approach to determine the variances on the estimated polynomial parameters and next on the resonance frequencies and damping ratios. The approach is based on the linearization of the sensitivity of the modal parameters to the noise variance. This noise variance (explicitly or as the coherence function) is assumed to be known a priori. The approach is tested on simulations and real-life measurements. [Copyright &y& Elsevier]

Abstract: A new approach to analyze the free and forced vibrations of beams with multiple cross-section steps is proposed using a composite element method in this paper. The results are compared to receptance function method and classical Rayleigh–Ritz method and finite element results. The natural frequencies obtained from the composite element method are found to be in close agreement with other methods mentioned above and finite element method. The forced vibration responses of the stepped beam are also calculated from the composite element method and compared with those obtained from the finite element method. Time histories from both methods are found to match very well. This indicates the correctness of the proposed method for vibration analyses of the stepped beam. The proposed method can be extended easily to deal with beams consisting of an arbitrary number of nonuniform segments. [Copyright &y& Elsevier]