Transfer matrix method for internal noise prediction of an arbitrary shell-cavity structure induced by temporal-spatial random surface excitation

Combining structural finite element method(FEM),acoustic finite element and boundary element methods,a model of elastic shell vibration of an arbitrary shell-cavity structure coupled with internal and external sound fields is built.In addition,the transfer matrices from the excitation force to vibration of the shell and internal sound field are calculated.As the fluctuating pressure of turbulent boundary layer(TBL) is a temporal-spatial random surface excitation,the overall shape function matrix is introduced,and then the relationship between power spectral density matrix of the generalized nodal force of the elastic shell and power spectral density of the temporal-spatial random surface excitation is derived.Utilizing the vibro-acoustic coupled transfer matrix,relationships between the power spectral densities of vibration of the elastic shell/internal sound field and the power spectral density matrix of the generalized nodal force are obtained.Thus,the calculation method of vibration and internal sound field of an arbitrary shell-cavity structure induced by temporal-spatial random surface excitation is established.A typical vibro-acoustic coupled model of a rectangular cavity with acoustic media internally and externally,and with elastic rectangular plate on one side,is taken as example.The vibration of the elastic shell and power spectral density of the internal sound field are calculated and compared with the analytical method.The two results generally agree with the analytical one,with deviations of about 1 dB and 2 dB,respectively.The transfer matrix method has good adaptability which is not restricted by the shell-cavity structure and the shape of the inner region.     

Modeling of micro-perforated panels in a complex vibro-acoustic environment using patch transfer function approach

A micro-perforated panel (MPP) with a backing cavity is a well known device for efficient noise absorption. This configuration has been thoroughly studied in the experimental conditions of an acoustic tube (Kundt tube), in which the MPP is excited by a normal incident plane wave in one dimension. In a more practical situation, the efficiency of MPP may be influenced by the vibro-acoustic behavior of the surrounding systems as well as excitation. To deal with this problem, a vibro-acoustic formulation based on the patch transfer functions (PTF) approach is proposed to model the behavior of a micro-perforated structure in a complex vibro-acoustic environment. PTF is a substructuring approach, which allows assembling different vibro-acoustic subsystems through coupled surfaces. Upon casting micro-perforations and the flexibility of the MPP under transfer function framework, the proposed PTF formulation provides explicit representation of the coupling between subsystems and facilitates physical interpretation. As an illustration example, application to a MPP with a backing cavity located in an infinite baffle is demonstrated. The proposed PTF formulation is finally validated through comparison with experimental measurements available in the literature.     

Vibro-acoustic behaviors of an elastically restrained double-panel structure with an acoustic cavity of arbitrary boundary impedance

An analytical study on the vibro-acoustic behaviors of a double-panel structure with an acoustic cavity is presented. Unlike the existing studies, a structural–acoustic coupling model of an elastically restrained double-panel structure with an acoustic cavity having arbitrary impedance on sidewalls around the cavity is developed in which the two dimensional (2D) and three dimensional (3D) modified Fourier series are used to represent the displacement of the panels and the sound pressure inside the cavity, respectively. The unknown expansions coefficients are treated as the generalized coordinates and the Rayleigh–Ritz method is employed to determine displacement and sound pressure solutions based on the energy expressions for the coupled structural–acoustic system. The effectiveness and accuracy of the present model is validated by numerical example and comparison with finite element method (FEM) and existing analytical method, with good agreement achieved. The influence of key parameters on the vibro-acoustic behaviors and sound transmission of the double-panel structure is investigated, including: cavity thickness, boundary conditions, sidewall impedance, and the acoustic medium in the cavity.     

Optimal poroelastic layer sequencing for sound transmission loss maximization by topology optimization method

Optimal layer sequencing of a multilayered acoustical foam is solved to maximize its sound transmission loss. A foam consisting of air and poroelastic layers can be optimized when a limited amount of a poroelastic material is allowed. By formulating the sound transmission loss maximization problem as a one-dimensional topology optimization problem, optimal layer sequencing and thickness were systematically found for several single and ranges of frequencies. For optimization, the transmission losses of air and poroelastic layers were calculated by the transfer matrix derived from Biot's theory. By interpolating five intrinsic parameters among several poroelastic material parameters, distinct air-poroelastic layer distributions were obtained; no filtering or postprocessing was necessary. The optimized foam layouts by the proposed method were shown to differ depending on the frequency bands of interest.     

传递矩阵法预报时空随机激励下任意薄壳腔体内部噪声

利用结构有限元结合声有限元及边界元方法,建立了任意薄壳腔体弹性壳板振动与内外声场的耦合模型,并计算了激励力与壳板振动和内部声场之间的传递矩阵;湍流边界层脉动压力具有时空随机面激励特性,引入整体形状函数矩阵,进一步推导弹性壳板广义节点力功率谱密度函数矩阵与随机面分布激励力功率谱密度函数的关系,再利用声振耦合传递矩阵,得到弹性壳板振动和内部声场功率谱密度函数与广义节点力功率谱密度函数矩阵的关系,形成随机分布激励下任意薄壳腔体结构振动及内部声场的计算方法。以典型的内外均有声介质且一面为弹性矩形板的矩形腔声振耦合模型为例,计算了弹性壳板振动和内部声场功率谱密度函数,并与解析方法进行了比较,两者基本吻合,偏差分别为1 dB和2 dB左右。传递矩阵法不受腔体结构及其内部区域形状的制约,具有良好的适用性。      

Vibro-acoustic analysis of a rectangular-like cavity with a tilted wall

In this paper, a fully coupled vibro-acoustic model is developed to characterize the structural and acoustic coupling of a flexible panel backed by a rectangular-like cavity with a slight geometrical distortion, which is introduced through a tilted wall. The combined integro-modal approach is used to handle the acoustic pressure inside the irregular-shaped cavity. Based on the model proposed, the distortion effect on the vibro-acoustic behavior of the coupled system is investigated using the averaged sound pressure level inside the enclosure and the averaged quadratic velocity of the vibrating plate. Simulations are conducted to examine the distortion effect on acoustic natural frequencies, acoustic pressures and structural responses. Effects of the wall inclination on coupling coefficients are also assessed, and an index is proposed to quantify the degree of variation of coupling strength.     

Unified multiphase modeling for evolving,acoustically coupled systems consisting of acoustic,elastic, poroelastic media and septa

This paper presents a new modeling technique that can represent acoustically coupled systems in a unified manner. The proposed unified multiphase (UMP) modeling technique uses Biot’s equations that are originally derived for poroelastic media to represent not only poroelastic media but also non-poroelastic ones ranging from acoustic and elastic media to septa. To recover the original vibro-acoustic behaviors of non-poroelastic media, material parameters of a base poroelastic medium are adjusted depending on the target media. The real virtue of this UMP technique is that interface coupling conditions between any media can be automatically satisfied, so no medium-dependent interface condition needs to be imposed explicitly. Thereby, the proposed technique can effectively model any acoustically coupled system having locally varying medium phases and evolving interfaces. A typical situation can occur in an iterative design process. Because the proposed UMP modeling technique needs theoretical justifications for further development, this work is mainly focused on how the technique recovers the governing equations of non-poroelastic media and expresses their interface conditions. We also address how to describe various boundary conditions of the media in the technique. Some numerical studies are carried out to demonstrate the validity of the proposed modeling technique.     

ZnO/Diamond/Si结构中声表面波传播特性分析

基于递归刚度矩阵方法, 建立了多层结构声表面波表面有效介电常数模型, 计算出了ZnO/Si结构声表面波的相速度频散特性, 与实验结果符合较好, 表明本文所建模型的准确性和有效性. 进一步计算得到了三层结构(ZnO/Diamond/Si)声表面波的相速度和机电耦合系数的频散规律, 获得此结构最优的高波速和高机电耦合系数组合及达到最优组合所需控制的变量, 为高频高性能声表面波器件设计和优化提供了有益参考. 关键词： 声表面波 多层结构 递归刚度矩阵 表面有效介电常数     

Prediction of the vibro-acoustic response of a structure-liner-fluid system based on a patch transfer function approach and direct experimental subsystem characterisation

The vibro-acoustic response of a structure-liner-fluid system is predicted by application of a patch transfer function (PTF) coupling scheme. In contrast to existing numerical approaches, PTF matrices of structure and liner are determined by a direct experimental approach, avoiding the requirement of material parameters. Emphasis is placed on poroelastic lining materials. The method accounts for surface input and next-neighbour transfer terms and for cross and cross-transfer terms through the specimen. Shear stresses and transfer terms to further patches on the liner are neglected. A single test-rig characterisation procedure for layered poroelastic media is proposed. The specimen is considered as a single component – no separation of layers is performed. For this reason the characterisation procedure can serve as a complement to existing methods if separation of layers is not possible and as a tool for validation of more detailed material models. Problem specific boundary conditions for skeleton and fluid, which may cause non-reciprocal cross terms, are dealt with by the procedure. Methods of measurement for the assessment of PTF matrices are presented and their accuracy and limitations are discussed. An air gap correction method for surface impedance measurements is presented.     

Effectiveness of T-shaped acoustic resonators in low-frequency sound transmission control of a finite double-panel partition

Double-panel partitions are widely used for sound insulation purposes. Their insulation efficiency is, however, deteriorated at low frequencies due to the structural and acoustic resonances. To tackle this problem, this paper proposes the use of long T-shaped acoustic resonators in a double-panel partition embedded along the edges. In order to facilitate the design and assess the performance of the structure, a general vibro-acoustic model, characterizing the interaction between the panels, air cavity, and integrated acoustic resonators, is developed. The effectiveness of the technique as well as the optimal locations of the acoustic resonators is examined at various frequencies where the system exhibits different coupling characteristics. The measured optimal locations are also compared with the predicted ones to verify the developed theory. Finally, the performance of the acoustic resonators in broadband sound transmission control is demonstrated.     

Deterministic-statistical analysis of a structural-acoustic system

The purpose of this paper is to develop an efficient approach for vibro-acoustic analysis. Being simple and representative, an exited plate-acoustic system is selected as a validation case for the vibro-acoustic analysis as the system presents one two-dimensional statistical component (modal dense structure panel—plate) connected to the other component (deterministic acoustic volume—cavity) through the area junction over a surface domain, rather than at a line boundary. Potential industrial applications of the system vibro-acoustic analysis would be in acoustic modelling of vehicle body panels such as the cabin roof panel, and door panels for the boom noise analysis.A new deterministic-statistical analysis approach is proposed from a combination or hybrid of deterministic analysis and statistical energy analysis (SEA) approaches. General theory of the new deterministic-statistical analysis approach is introduced. The main advantage of the new deterministic-statistical analysis approach is its possibility in place of the time consuming Monte Carlo simulation. In order to illustrate and validate the new deterministic-statistical analysis approach, three approaches of the deterministic analysis, the statistical energy analysis and the new deterministic-statistical analysis are then applied to conduct the plate-acoustic system modelling, and their results will be compared. The vibro-acoustic energy coupling characteristic of the plate-acoustic system will be studied. The most suitable frequency range for the new approach will be identified in consideration of computational accuracy, information and speed.     

Sound transmission through finite lightweight multilayered structures with thin air layers

The sound transmission loss (STL) of finite lightweight multilayered structures with thin air layers is studied in this paper. Two types of models are used to describe the vibro-acoustic behavior of these structures. Standard transfer matrix method assumes infinite layers and represents the plane wave propagation in the layers. A wave based model describes the direct sound transmission through a rectangular structure placed between two reverberant rooms. Full vibro-acoustic coupling between rooms, plates, and air cavities is taken into account. Comparison with double glazing measurements shows that this effect of vibro-acoustic coupling is important in lightweight double walls. For infinite structures, structural damping has no significant influence on STL below the coincidence frequency. In this frequency region, the non-resonant transmission or so-called mass-law behavior dominates sound transmission. Modal simulations suggest a large influence of structural damping on STL. This is confirmed by experiments with double fiberboard partitions and sandwich structures. The results show that for thin air layers, the damping induced by friction and viscous effects at the air gap surfaces can largely influence and improve the sound transmission characteristics.     

三层平板结构声能流计算及传输规律

为了理解多层有源隔声结构的物理机理,同时优化被动隔声结构,需深入分析三层结构中声能量的传输规律。首先对三层板腔结构建模并求解系统的振动响应,然后用数值方法求解平板向封闭空间辐射声的声传输阻抗,并计算各层结构的辐射声功率。最后,通过分析各子系统所占的能量及各层结构四类模态组辐射声功率的变化获得声能量的传输规律。结果表明,按模态类型的不同,能量传输可等效认为存在四个传输通道,各通道的能量传输具有相似的带通特性,其成因在于不同的平板与空腔模态对的耦合强弱不同。      

Virtual sensors for active noise control in acoustic-structural coupled enclosures using structural sensing: part II--Optimization of structural sensor placement

The work proposed an optimization approach for structural sensor placement to improve the performance of vibro-acoustic virtual sensor for active noise control applications. The vibro-acoustic virtual sensor was designed to estimate the interior sound pressure of an acoustic-structural coupled enclosure using structural sensors. A spectral-spatial performance metric was proposed, which was used to quantify the averaged structural sensor output energy of a vibro-acoustic system excited by a spatially varying point source. It was shown that (i) the overall virtual sensing error energy was contributed additively by the modal virtual sensing error and the measurement noise energy; (ii) each of the modal virtual sensing error system was contributed by both the modal observability levels for the structural sensing and the target acoustic virtual sensing; and further (iii) the strength of each modal observability level was influenced by the modal coupling and resonance frequencies of the associated uncoupled structural/cavity modes. An optimal design of structural sensor placement was proposed to achieve sufficiently high modal observability levels for certain important panel- and cavity-controlled modes. Numerical analysis on a panel-cavity system demonstrated the importance of structural sensor placement on virtual sensing and active noise control performance, particularly for cavity-controlled modes.     

Calculation of electromechanical coupling coefficient of Lamb waves in multilayered plates

Two methods have been always used to calculate the electromechanical coupling coefficient of a Lamb wave in a multilayered plate: one is an approximate method using the acoustic velocity difference under different electric boundary conditions and the other is the Green's function method. The Green's function method is more accurate but more complicated, because an 8N-order matrix is used for calculating the electromechanical coupling coefficient of the Lamb wave in an N-layered plate, which induces great computation loads and some calculation deviations. In this paper, a transfer matrix method is used for calculating the electromechanical coupling coefficient of Lamb waves in a multilayered plate, in which only an 8-order matrix is needed regardless of the number of layers of the plate. The results show that the transfer matrix method can obtain the same accuracy as those by the Green's function method, but the computation load and deviation are greatly decreased by avoiding the use of a high order matrix used in the Green's function method.     

含空气层与多孔材料的复合结构隔声特性研究

基于高速列车减振降噪需求,本文应用Biot提出的多孔弹性介质声传播理论,采用传递矩阵法理论推导了典型分层结构的隔声量计算公式,给出了空气层与多孔材料对分层复合结构隔声特性的影响。将传递矩阵与遗传算法相结合,对特定中低频段内的复合结构隔声特性进行了优化。研究结果表明:空气层和多孔材料有助于分层复合结构隔声量的提高,特别是空气层对低频隔声有很好的促进作用,另外空气层与多孔材料的分配情况也影响着隔声效果。含有空气层的复合结构在提高隔声量的同时降低了结构的总体重量,实现了高速列车隔声材料低能耗和轻量化的设计目标。     

Noise control of an acoustic enclosure covered by a double-wall structure with shallow gap: Design of resonator-like cavities

The present study addresses the possibility of using resonator-like cavities for noise attenuation of an acoustic enclosure covered by a double-wall structure with shallow gap. Different from the conventional design of using Helmholtz resonators, a set of coupled equation describing resonator-like cavity is integrated into the vibro-acoustic model, under which the modes in a broad frequency range will be controlled. Based on the tuned weighting coefficient and the acoustic potential energy, an objective function is developed to optimize parameters (number and location) of resonator-like cavities. The effect of shallow gap on the first two dominant modes of the coupled system and energy transmission is investigated. Simulation results indicate the effectiveness of the proposed method for noise attenuation, which might be of direct benefit to engineering applications.     

Stable reformulation of transfer matrix method for wave propagation in layered anisotropic media.

The numerical instability problem in the standard transfer matrix method has been resolved by introducing the layer stiffness matrix and using an efficient recursive algorithm to calculate the global stiffness matrix for an arbitrary anisotropic layered structure. For general anisotropy the computational algorithm is formulated in matrix form. In the plane of symmetry of an orthotropic layer the layer stiffness matrix is represented analytically. It is shown that the elements of the stiffness matrix are as simple as those of the transfer matrix and only six of them are independent. Reflection and transmission coefficients for layered media bounded by liquid or solid semi-spaces are formulated as functions of the total stiffness matrix elements. It has been demonstrated that this algorithm is unconditionally stable and more efficient than the standard transfer matrix method. The stiffness matrix formulation is convenient in satisfying boundary conditions for different layered media cases and in obtaining modal solutions. Based on this method characteristic equations for Lamb and surface waves in multilayered orthotropic media have been obtained. Due to the stability of the stiffness matrix method, the solutions of the characteristic equations are numerically stable and efficient. Numerical examples are given.     

Hybrid compliance-stiffness matrix method for stable analysis of elastic wave propagation in multilayered anisotropic media

This paper presents the hybrid compliance-stiffness matrix method for stable analysis of elastic wave propagation in multilayered anisotropic media. The method utilizes the hybrid matrix of each layer in a recursive algorithm to deduce the stack hybrid matrix for a multilayered structure. Like the stiffness matrix method, the hybrid matrix method is able to eliminate the numerical instability of transfer matrix method. By operating with total stresses and displacements, it also preserves the convenience for incorporating imperfect or perfect interfaces. However, unlike the stiffness matrix, the hybrid matrix remains to be well-conditioned and accurate even for zero or small thicknesses. The stability of hybrid matrix method has been demonstrated by the numerical results of reflection and transmission coefficients. These results have been determined efficiently based on the surface hybrid matrix method involving only a subset of hybrid submatrices. In conjunction with the recursive asymptotic method, the hybrid matrix method is self-sufficient without hybrid asymptotic method and may achieve low error level over a wide range of sublayer thickness or the number of recursive operations.     

Vibro-acoustic behaviour of laminated double glazing enclosing a viscothermal fluid cavity

This paper presents a new numerical model to investigate the vibro-acoustic behaviour of two laminated glass plates enclosing a thin viscothermal fluid cavity. The aim of this work is to develop an original five layer (two skins plies, two adhesive films and a core ply) laminated plate finite element by mixing Kirchhoff and Mindlin plate’s theory. The formulation is based on the theory that accounts for the transverse shear in the adhesive films and in the core. The acousto-elastic model is established in dimensionless appropriate form including the effects of viscosity and thermal conductivity of fluid and by taking into account the fluid-structure interaction. The discretization of the energy functional by finite element method gives after minimisation a symmetrical coupled matrix system in which the acoustic matrices are frequency dependent. Therefore, an iterative procedure is derived to determine the eigenmodes of the coupled system. The modal approach is adopted to determine the vibro-acoustic system’s response. Then, the validation of the new laminate finite element model is achieved by comparing the sandwich plate results against data obtained from literature. Subsequently, predicted responses, such as the vibration transmissibility and the transmission loss of the coupled system, for a given laminated double glazing under an imposed homogeneous pressure are presented and discussed. Numerical results show the importance of both lamination and viscothermal fluid effects on double glazing vibro-acoustic behaviour.