Active vibration control for structural-acoustic coupling system of a 3-D vehicle cabin model

This paper presents an active vibration control system for use with structural-acoustic coupling system using piezoelectric actuators and piezoelectric sensors. For modelling a complicated 3-D vehicle cabin model, the structural-acoustic coupling system is analyzed by combining the structural data from modal testing with the acoustic data from the finite element method. Through the structural-acoustic analysis program, the control plate and the control modes are selected, which are most effective for attenuating its noise. A robust LQG controller with two sensor signal filters is designed to remove the experimental problems such as the spillover effect due to uncontrolled modes. The robust LQG controller for the structural-acoustic coupling system can reduce the interior noise of the cavity as well as the structural vibration of the cabin.     

Analytical research on structural-acoustic coupling of a cavity surrounded by flexible panel

The structural-acoustic coupling characteristics, mechanisms, effect of structural-acoustic coupling on natural mode and natural frequencies of the system are analyzed theoretically and numerically. Formulae for the natural frequencies of the coupled system are derived. Some new conclusions are obtained. Analytical results demonstrate that the strongly coupled system indicates obvious closed-loop feedback characteristics, whereas the weakly coupled system indicates obvious feedforward characteristics, and it is because of the presence of the feedback loop that the natural characteristics and natural frequencies are changed. Cluster coupling characteristic between the structural and acoustic modes for the regular cavity and panel system is found, which determines the coupling interaction between the flexible panel and cavity. Any mode in one mode cluster only interferes the modes and the modal natural frequencies in the same cluster independently. The modal cluster coupling changes not only the natural frequencies of the system but also the modal order and structural mode shape.     

封闭声腔的结构-声耦合的瞬态响应及固有特性分析的时域有限体积法

基于波动理论,采用时域有限体积法(TDFVM)研究封闭声腔结构-声耦合问题的瞬态响应及固有特性。该方法在结构与流体区域分别求解结构动力学方程与非均匀介质中的声波动方程,根据流固分界面上的力平衡与质点振速连续条件实现结构-声耦合。通过数值算例验证方法的正确性和精确性,在此基础上研究封闭声腔结构与空气耦合的瞬态响应及固有特性,分析水深变化对耦合系统声振特性和固有特性的影响。结果表明,随着水深的增加,结构与水的耦合会更加强烈,导致耦合系统的特征频率降低,同时空气腔深度的减小,导致声腔的部分固有频率增加。该法对计算机内存要求低,且可以考虑含有非均匀流体的结构-声耦合。      

Structural-acoustic finite element analysis of the automobile passenger compartment: A review of current practice

This paper contains a brief review of the formulation of the finite element method for structural-acoustic analysis of an enclosed cavity, and illustrations are given of the application of this analytical method at General Motors Corporation to investigate the acoustics of the automobile passenger compartment. Low frequency noise in the passenger compartment (in approximately the 20–200 Hz frequency range) is of primary interest, and particularly that noise which is generated by the structural vibration of the wall panels of the compartment. The topics which are covered in the paper include the computation of acoustic modes and resonant frequencies of the passenger compartment, the effect of flexible wall panels on the cavity acoustics, the methods of direct and modal coupling of the structural and acoustic vehicle systems, and forced vibration analysis illustrating the techniques for computing panel-excited noise and for identifying critical panels around the passenger compartment. The capabilities of the finite element method are illustrated by applications to the production automobile, and experimental verifications of the various techniques are presented to illustrate the accuracy of the method.     

FEM Modal Analysis on the Gravity Support System of ITER

The three-dimensional finite element method model with 20 degree sector of the ITER overall gravity support system was built by the ANSYS software. The modal analysis of the gravity support system was made and first ten natural frequencies and vibration modes of the gravity support system were calculated by using Block Lanczos method. The results of modal analysis on ITER represent that the stiffness of flexible plates has influenced greatly for the natural frequency of the system.     

Time domain finite volume method for the transient response and natural characteristics of structural-acoustic coupling in an enclosed cavity

A time domain finite volume method（TDFVM）based on wave theory is developed to analyze the transient response and natural characteristics of structural-acoustic coupling problems in an enclosed cavity.In the present method,the elastic dynamic equations and acoustic equation in heterogeneous medium are solved in solid domains and fluid domains respectively.The structural-acoustic coupling is implemented according to the continuity condition of the particle velocity along the normal direction and the normal traction equilibrium condition on the interface.Several numerical examples are presented to validate the effectiveness and accuracy of the present TDFVM.Then the effects of water depth on the acoustic and vibration characteristics and the natural characteristics of a structural-acoustic coupling system are analyzed.The numerical results show that the increase of water depth leads to a stronger coupling between the water and structure and the decrease of natural frequencies of coupling system,The computational cost and memory of this method are small and it can be applicable to structural-acoustic coupling problems in the heterogeneous fluid.     

Hybrid holographic-numerical method for modal analysis of complex structures

This paper presents a hybrid holographic-numerical method for modal analysis of complex structures. A continuous structure is first lumped into a number of discrete elements to form an elastically connected lumped linear system. The matrix of influence coefficients of the lumped linear system are then determined by exerting a static load to the element centers and measuring the corresponding whole-field displacement using digital holographic interferometry. The eigenvalues and eigenvectors of the influence coefficients, which in a physical sense represent the natural frequencies and mode shapes of the structure, are then calculated using the numerical method. A major advantage of the proposed hybrid method is that it is not necessary to know the Young's modulus, the Poisson's ratio of the material and the boundary conditions, as the displacement field measured by the optical method has automatically reflected the real boundary conditions and the material properties, which makes this method particularly useful for studying objects made from anisotropic materials such as composites. Another advantage of the proposed method is that structures of any complex and irregular shape will not increase the complexity of the characterization process. The proposed is also suitable for experimentally validating the modal analysis results from finite element method models.     

Modeling and Measurement of a Tunable Acoustoelastic System

Acoustoelastic coupling occurs when a hollow structure’s in-vacuo mode aligns with an acoustic mode of the internal cavity. The impact of this coupling on the total dynamic response of the structure can be quite severe depending on the similarity of the modal frequencies and shapes. Typically, acoustoelastic coupling is not a design feature, but rather an unintended result that must be remedied as modal tests of structures are often used to correlate or validate finite element models of the uncoupled structure. Here, however, a test structure is intentionally designed such that multiple structural and acoustic modes are well-aligned, resulting in a coupled system that allows for an experimental investigation. First, coupling in the system is identified using a measure termed the magnification factor. Next, the structural-acoustic interaction is measured. Modifications to the system demonstrate the dependency of the coupling on changes in the mode shape and frequency proximity. This includes an investigation of several practical techniques used to decouple the system by altering the internal acoustic cavity, as well as the structure itself. These results show that acoustic absorption material effectively decoupled the structure while structural modifications, in their current form, proved unsuccessful. Readily available acoustic absorptive material was effective in reducing the coupled effects while presumably adding negligible mass or stiffness to the structure.     

An extended transfer matrix-finite element method for free vibration of plates

A combination of extended transfer matrix and finite element methods is proposed for obtaining vibration frequencies of structures. This method yields the value of the frequency once a trial value is assumed. By using this technique, the number of nodes required in the regular finite element method is reduced and therefore a smaller computer can be used. Besides, no plotting of the values of the determinants corresponding to each assumed frequency is necessary. A worked example is given for the case of vibration of a cantilever plate. The results show fast convergence from the assumed value to the true natural frequency.     

Numerical Investigation on Vibration Performance of Flexible Plates Actuated by Pneumatic Artificial Muscle

This paper theoretically introduced the feasibility of changing the vibration characteristics of flexible plates by using bio-inspired, extremely light, and powerful Pneumatic Artificial Muscle (PAM) actuators. Many structural plates or shells are typically flexible and show high vibration sensitivity. For this reason, this paper provides a way to achieve active vibration control for suppressing the oscillations of these structures to meet strict stability, safety, and comfort requirements. The dynamic behaviors of the designed plates are modeled by using the finite element (FE) method. As is known, the output force vs. contraction curve of PAM is nonlinear generally. In this present finite element model, the maximum forces provided by PAM in different air pressure are adopted as controlling forces for applying for the plate. The non-linearity between the output force and displacement of PAM is avoided in this study. The dynamic behaviors of plates with several independent groups of controlling forces are observed and studied. The results show that the natural frequencies of the plate can be varying and the max amplitude decreases significantly if the controlling forces are applied. The present work also demonstrates the potential of the PAM actuators as valid means for damping out the vibration of flexible systems.     

A damping mechanics model and a beam finite element for the free-vibration of laminated composite strips under in-plane loading

A theoretical framework is presented for predicting the nonlinear damping and damped vibration of laminated composite strips due to large in-plane forces. Nonlinear Green-Lagrange axial strains are introduced in the governing equations of a viscoelastic composite and new nonlinear damping and stiffness matrices are formulated including initial stress effects. Building upon the nonlinear laminate mechanics, a damped beam finite element is developed. Finite element stiffness and damping matrices are synthesized and the static equilibrium is predicted using a Newton-Raphson solver. The corresponding linearized damped free-vibration response is predicted and modal frequencies and damping of the in-plane deflected strip are calculated. Numerical results quantify the nonlinear effect of in-plane loads on structural modal damping of various laminated composite strips. The modal loss-factors and natural frequencies of cross-ply Glass/Epoxy beams subject to in-plane loading are measured and correlated with numerical results.     

Vibro-acoustic design sensitivity analysis using the wave-based method

Conventional element-based methods, such as the finite element method (FEM) and boundary element method (BEM), require mesh refinements at higher frequencies in order to converge. Therefore, their applications are limited to low frequencies. Compared to element-based methods, the wave-based method (WBM) adopts exact solutions of the governing differential equation instead of simple polynomials to describe the dynamic response variables within the subdomains. As such, the WBM does not require a finer division of subdomains as the frequency increases in order to exhibit high computational efficiency. In this paper, the design sensitivity formulation of a semi-coupled structural-acoustic problem is implemented using the WBM. Here, the results of structural harmonic analyses are imported as the boundary conditions for the acoustic domain, which consists of multiple wave-based subdomains. The cross-sectional area of each beam element is considered as a sizing design variable. Then, the adjoint variable method (AVM) is used to efficiently compute the sensitivity. The adjoint variable is obtained from structural reanalysis using an adjoint load composed of the system matrix and an evaluation of the wave functions of each boundary. The proposed sensitivity formulation is subsequently applied to a two-dimensional (2D) vehicle model. Finally, the sensitivity results are compared to the finite difference sensitivity results, which show good agreement.     

Dynamic stability of a sandwich plate with a constraining layer and electrorheological fluid core

The dynamic stability problems of a sandwich plate with a constraining layer and an electrorheological (ER) fluid core subjected to an axial dynamic force are investigated. The rectangular plate is covered in an ER fluid core and a constraining layer to improve the stability of the system. Effects of the natural frequencies, static buckling loads, and loss factors on the dynamic stability behavior of the sandwich plate are studied in the paper. Rheological property of an ER material, such as viscosity, plasticity, and elasticity may be changed when applying an electric field. The modal damper and the natural frequencies for the sandwich plate are calculated for various electric fields. When an electric field is applied, the damping of the system is more effective. In this study, finite element method and the harmonic balance method are used to calculate the instability regions of the sandwich plate. The ER fluid core is found to have a significant effect on the dynamic stability regions.     

Analytical prediction of break-out noise from a reactive rectangular plenum with four flexible walls

This paper describes an analytical calculation of break-out noise from a rectangular plenum with four flexible walls by incorporating three-dimensional effects along with the acoustical and structural wave coupling phenomena. The breakout noise from rectangular plenums is important and the coupling between acoustic waves within the plenum and structural waves in the flexible plenum walls plays a critical role in prediction of the transverse transmission loss. The first step in breakout noise prediction is to calculate the inside plenum pressure field and the normal flexible plenum wall vibration by using an impedance-mobility approach, which results in a compact matrix formulation. In the impedance-mobility compact matrix (IMCM) approach, it is presumed that the coupled response can be described in terms of finite sets of the uncoupled acoustic subsystem and the structural subsystem. The flexible walls of the plenum are modeled as an unfolded plate to calculate natural frequencies and mode shapes of the uncoupled structural subsystem. The second step is to calculate the radiated sound power from the flexible walls using Kirchhoff-Helmholtz (KH) integral formulation. Analytical results are validated with finite element and boundary element (FEM-BEM) numerical models.     

A modal disturbance estimator for vibration suppression in nonlinear flexible structures

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.     

Vibrations of a polygonal plate having orthogonal straight edges by an extended rayleigh-ritz method

An extended Rayleigh-Ritz method is presented for solving vibration problems of a polygonal plate having orthogonal straight edges. The polygonal plate is considered as an assemblage of several rectangular plates. For each element rectangular plate, the transverse displacement is approximated by interpolation functions corresponding to unknown displacements and slopes at the discrete points which are chosen along the edges, and series of trial functions which satisfy homogeneous artificial boundary conditions. By minimizing the energy functional corresponding to the assumed displacement function, the dynamic stiffness matrix of the element rectangular plate, which is similar to that obtained in the finite element method, is derived. The dynamic stiffness matrix of the whole system is obtained by summing up those of the element rectangular plates. Numerical results are presented for the natural frequencies and mode shapes of cantilever L-shaped and T-shaped plates.     

A NEW METHOD FOR IN-PLANE VIBRATION ANALYSIS OF CIRCULAR RINGS WITH WIDELY DISTRIBUTED DEVIATION

A new analytical method was developed to predict the in-plane mode shapes and the natural frequencies of a ring with widely distributed deviation. The Laplace transform was used to find the exact solution of eigenvalue problem without assuming any trial functions and finite elements. The widely distributed deviation was effectively formulated in the theory using Gauss-Legendre quadrature. The validity of the proposed method was examined through finite element analysis and modal test. The effects of partial change of the density, the stiffness, and the thickness on the natural frequencies of the ring were investigated.     

Vibration and damping analysis of annular plates with constrained damping layer treatments

The natural frequencies and modal loss factors of annular plates with fully and partially constrained damping treatments are considered. The equations of free vibration of the plate including the transverse shear effects are derived by a discrete layer annular finite element method. The extensional and shear moduli of the viscoelastic material layer are described by the complex quantities. Complex eigenvalues are then found numerically, and from these, both frequencies and loss factors are extracted. The effects of viscoelastic layer stiffness and thickness, constraining layer stiffness and thickness, and treatment size on natural frequencies and modal loss factors are presented. Numerical results also show that the longer constrained damping treatment in radial length does not always provide better damping than the shorter ones.     

STRUCTURAL DAMAGE DETECTION BASED ON A MICRO-GENETIC ALGORITHM USING INCOMPLETE AND NOISY MODAL TEST DATA

This paper describes a procedure for detecting structural damage based on a micro-genetic algorithm using incomplete and noisy modal test data. As the number of sensors used to measure modal data is normally small when compared with the degrees of freedom of the finite element model of the structure, the incomplete mode shape data are first expanded to match with all degrees of freedom of the finite element model under consideration. The elemental energy quotient difference is then employed to locate the damage domain approximately. Finally, a micro-genetic algorithm is used to quantify the damage extent by minimizing the errors between the measured data and numerical results. The process may be either of single-level or implemented through two-level search strategies. The study has covered the use of frequencies only and the combined use of both frequencies and mode shapes. The proposed method is applied to a single-span simply supported beam and a three-span continuous beam with multiple damage locations. In the study, the modal test data are simulated numerically using the finite element method. The measurement errors of modal data are simulated by superimposing random noise with appropriate magnitudes. The effectiveness of using frequencies and both frequencies and mode shapes as the data for quantification of damage extent are examined. The effects of incomplete and noisy modal test data on the accuracy of damage detection are also discussed.     

A coupled edge-/face-based smoothed finite element method for structural-acoustic problems

The edge-based smoothed finite element method (ES-FEM) and the face-based smoothed finite element method (FS-FEM) developed recently have shown great efficiency in solving solid mechanics problems with triangular and tetrahedral meshes. In this paper, a coupled ES-/FS-FEM model is extended to solve the structural-acoustic problems consisting of a plate structure interacting with the fluid medium. Three-node triangular elements and four-node tetrahedral elements are used to discretize the two-dimensional (2D) plate and three-dimensional (3D) fluid, respectively, as they can be generated easily and even automatically for complicated geometries. The field variable in each element is approximated using the linear shape functions, which is exactly the same as that in the standard FEM. The gradient field of the problem is obtained particularly using the gradient smoothing operation over the edge-based and face-based smoothing domains in 2D and 3D, respectively. The gradient smoothing technique can provide a proper softening effect to the model, effectively solve the problems caused by the well-known “overly-stiff” phenomenon existing in the standard FEM, and hence significantly improve the accuracy of the solution for the coupled systems. Intensive numerical studies have been conducted to verify the effectiveness of the coupled ES-/FS-FEM for structural-acoustic problems.