Structural acoustic silencers--design and experiment

The effectiveness of introducing flexible structural layers into air conveying ducts for controlling noise is investigated through theoretical and experimental means, focusing at low frequencies where conventional passive silencing technology is least effective. Previous theoretical work has shown that using flexible rather than rigid walls has the potential to achieve high transmission losses. The physical mechanisms responsible for structural acoustic silencing, including the relation between transmission loss peaks and structural resonance corresponding to different transverse structural modes, are presented. Sensitivity of the performance to acoustic and structural boundary conditions is discussed. To eliminate radiated noise from these walls (breakout noise), a rigid walled cavity is introduced under the flexible plate. The challenge is to find means to reject plane waves in the two-duct system. Designs that overcome these issues and achieve appreciable transmission loss are investigated. Results based on three-dimensional finite element simulations are compared with experimental results.     

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.     

Simulative and experimental investigations on pressure-induced structural vibrations of a rear muffler

The periodically blown out exhaust gas of a combustion engine may excite structural vibrations of the exhaust system. In addition to the noise of the orifice, these vibrations contribute to the overall noise radiation of the exhaust system. In this work, the excitation of structural vibrations of a rear muffler via the acoustic path is investigated both in experiments and simulations. In both cases transfer functions from the acoustic pressure at the inlet to the structural deflection on the surface of the rear muffler are determined and compared to each other. For the simulation an FE-FE (finite element) coupling is applied to account for the fluid-structure interaction. To efficiently predict the fluid-structure coupled behavior, a model reduction technique for the finite element method based on the Craig-Bampton method and the Rubin method is presented. In a last step, the sound radiation is evaluated by solving the exterior acoustic problem with the fast multipole boundary element method. For this purpose, the results of the FE computation are used as boundary datum.     

双层板腔结构声传输及其有源控制研究

利用子系统模态综合方法,结合阻抗-导纳矩阵法,建立了双层板腔结构向自由空间声传输及其在入射板PZT控制、辐射板PZT控制,和腔中次级声源作动等多种控制策略下,系统物理模型的统一的分析模型,导出了系统模态响应及最优次级源强度的统一的阻抗-导纳矩阵表达式。该模型表达式各部分物理意义清晰、明确,便于进行系统耦合理论、有源控制及其机理的分析和数值研究。然后,在此基础上对双层板腔结构声传输有源控制进行了全面深入的数值计算和分析研究,重点探讨了控制方法策略及系统参数对有源控制效果的影响及其对应的控制机理。结果表明:入射板PZT作动辐射声功率最小控制策略是通过入射板、声腔和辐射板三个子系统的模态抑制或重组达到消声的目的,涉及多种复杂控制机理,对入射板、辐射板和声腔模态均有效,但对入射板模态更有效;在低频段声腔(0,0,0)模态在系统耦合响应中起主导作用,因此利用腔中次级声源作动能获得较理想的控制效果,是一种较好的控制策略;由于声腔模态与结构模态间复杂的耦合关系,使得某些频率处腔中声势能一定程度上的降低并不一定导致系统声传输损失的增加,因此,腔中声势能最小控制策略不一定能够获得理想的声传输控制效果。      

A Legendre spectral element model for sloshing and acoustic analysis in nearly incompressible fluids

A new spectral finite element formulation is presented for modeling the sloshing and the acoustic waves in nearly incompressible fluids. The formulation makes use of the Legendre polynomials in deriving the finite element interpolation shape functions in the Lagrangian frame of reference. The formulated element uses Gauss–Lobatto–Legendre quadrature scheme for integrating the volumetric stiffness and the mass matrices while the conventional Gauss–Legendre quadrature scheme is used on the rotational stiffness matrix to completely eliminate the zero energy modes, which are normally associated with the Lagrangian FE formulation. The numerical performance of the spectral element formulated here is examined by doing the inf–sup test on a standard rectangular rigid tank partially filled with liquid. The eigenvalues obtained from the formulated spectral element are compared with the conventional equally spaced node locations of the h-type Lagrangian finite element and the predicted results show that these spectral elements are more accurate and give superior convergence. The efficiency and robustness of the formulated elements are demonstrated by solving few standard problems involving free vibration and dynamic response analysis with undistorted and distorted spectral elements, and the obtained results are compared with available results in the published literature.     

Sound transmission in pipes with porous walls

Pipes with porous (permeable) walls have received the attention of several authors as a noise control element in automotive intake systems; however, a closed theory of sound transmission including the effect of the coupling of the internal and external acoustic fields and the presence of mean flow does not appear to be available. The present paper proposes an integro-differential system for the propagation of plane sound waves in pipes with porous walls, and presents its general numerical solution, as well as an approximate analytical solution. The predicted effect of the coupling between the internal and external acoustic fields in a circular pipe made of reinforced woven fabric walls is shown, and the transmission loss predictions are compared with the existing experimental data in the literature.     

Free vibration analysis of ribbed plates by a combined analytical–numerical method

An easy to code and computationally efficient analytical–numerical method for quick prediction of the modal characteristics of rectangular ribbed plates is presented. The approach is suitable for low-frequency free vibration analysis of thin rectangular plates reinforced by a small number of light stiffeners. The assumed-modes method is used to formulate the equations of motion of the plate and the rib separately. The motion of the built-up structure is then obtained by enforcing appropriate continuity conditions between the two. The resulting sparse generalized eigenvalue problem can be profitably solved by reliable methods to calculate only a small set of selected eigenmodes. An alternative formulation is also proposed for the single-ribbed case which leads to a compact analytical form of the frequency equation whose solution can be easily determined either graphically or numerically. The present method demonstrates good agreement with published results and standard finite element analysis.     

声表面波在厚金属栅阵中的耦合模参数

提出了一种研究声表面波在压电晶体厚金属栅阵中传播特性的理论方法。将有限元和声表面波在周期栅阵中的变分原理分析方法相结合,在陈东培和H.A.Haus理论基础上、用有限元分析金属短路栅对声表面波传输特性的影响,将力学负载贡献的耦合模参数用有限元矩阵表示,使其适用于声表面波在厚金属或任意形状栅条中传输情况,给出了具体理论分析方法和相应的理论表达式。最后,具体研究了几种压电晶体上金、铝或银栅阵中声表面波的传输特性,通过数值计算给出了声表面波的耦合模参数。      

Perturbation of fluid-guided waves induced by bending plates

In order to discover whether the interaction between flexural and dilatational waves in a fluid-filled rectangular duct may be the reason why one observes experimentally a dispersion in the speed of the plane wave inside the duct, a calculation is carried out by the finite element method both in the structure and in the fluid. The numerical results of the coupling problem agree qualitatively with the phenomenon observed, and it appears that the usual hypothesis of local reaction of the walls does not apply in all frequency ranges.     

Energy flow analysis and design sensitivity of structural problems at high frequencies

The design sensitivity formulation of an energy finite element method is presented using the direct differentiation and adjoint variable methods. The continuum method is used to derive the design sensitivity equation of the energy flow equation, whereas the discrete method is used to calculate the variation of the coupling relation. For design variables, material property, panel thickness, and structural shape are taken into account, in addition to the structural damping factor. The design variable's effect on the power transfer coefficient is discussed in detail. Even if the system matrix equation is not symmetric, the adjoint problem is solved using the same factorized matrix from response analysis. Design sensitivity results calculated from the proposed method are compared to the finite difference sensitivity results with a good agreement.     

有限元-统计能量分析法的拖拉机驾驶室噪声研究*

对某拖拉机驾驶室内中频噪声进行预测,建立了拖拉机驾驶室FE-SEA(有限元统计能量分析)混合模型,通过理论计算和试验方法获取驾驶室结构内损耗因子等数据；加载振动和噪声激励后进行有限元-统计能量分析联合仿真,将仿真获取的驾驶室声压级与实测数据进行对比,分析对比表明该模型在中频段利用FE-SEA混合法分析所得结果与试验测试值拟合程度较高,分析各子系统对驾驶室声腔的能量贡献度,确定对驾驶室噪声贡献较大的子系统,针对性对驾驶室声学包进行整改,获得一定降噪效果。     

Structural-acoustic coupling effect on the nonlinear natural frequency of a rectangular box with one flexible plate

The nonlinear natural frequency of a rectangular box, which consists of one flexible plate and five rigid plates, is studied in this paper. The flexible plate is assumed to vibrate like a simple piston. The behavior of the structural-acoustic coupling between the flexible plate and the air cavity is analyzed by using the proposed finite element modal method. The system finite element equation is reduced and expressed in terms of the modal coordinates with small degrees of freedom by using the proposed reduction method. The system nonlinear stiffness matrix representing the large amplitude vibration can be transformed to be a constant modal matrix. The natural frequencies are determined by using the harmonic balance method to solve the eigenvalue equations of the structural-acoustic system. The effect of the cavity depth on the natural frequencies and convergence studies are discussed in detail.     

Noise Prediction in Subsonic Flow Using Seventh-Order Dissipative Compact Scheme on Curvilinear Mesh

In this paper, we investigate the performance of the seventh-order hybrid cell-edge and cell-node dissipative compact scheme (HDCS-E8T7) on curvilinear mesh for noise prediction in subsonic flow. In order to eliminate the errors due to surface conservation law (SCL) is dissatisfied with curvilinear meshes, the symmetrical conservative metric method (SCMM) is adopted to calculate the grid metric derivatives for the HDCS-E8T7. For the simulation of turbulence flow which may have main responsibility for the noise radiation, the new high-order implicit large eddy simulation (HILES) based on the HDCS-E8T7 is employed. Three typical cases, i.e., scattering of acoustic waves by multiple cylinder, sound radiated from a rod-airfoil and subsonic jet noise from nozzle, are chosen to investigate the performance of the new scheme for predicting aeroacoustic problem. The results of scattering of acoustic waves by multiple cylinder indicate that the HDCS-E8T7 satisfying the SCL has high resolution for the aeroacoustic prediction. The potential of the HDCS-E8T7 for aeroacoustic problems on complex geometry is shown by the predicting sound radiated from a rod-airfoil configuration. Moreover, the subsonic jet noise from nozzle has been successfully predicted by the HDCS-E8T7.     

Development of a 3D finite element acoustic model to predict the sound reduction index of stud based double-leaf walls

Building standards incorporating quantitative acoustical criteria to ensure adequate sound insulation are now being implemented. Engineers are making great efforts to design acoustically efficient double-wall structures. Accordingly, efficient simulation models to predict the acoustic insulation of double-leaf wall structures are needed. This paper presents the development of a numerical tool that can predict the frequency dependent sound reduction index R of stud based double-leaf walls at one-third-octave band frequency range. A fully vibro-acoustic 3D model consisting of two rooms partitioned using a double-leaf wall, considering the structure and acoustic fluid coupling incorporating the existing fluid and structural solvers are presented. The validity of the finite element (FE) model is assessed by comparison with experimental test results carried out in a certified laboratory. Accurate representation of the structural damping matrix to effectively predict the R values are studied. The possibilities of minimising the simulation time using a frequency dependent mesh model was also investigated. The FEA model presented in this work is capable of predicting the weighted sound reduction index R_w along with A-weighted pink noise C and A-weighted urban noise C_tr within an error of 1 dB. The model developed can also be used to analyse the acoustically induced frequency dependent geometrical behaviour of the double-leaf wall components to optimise them for best acoustic performance. The FE modelling procedure reported in this paper can be extended to other building components undergoing fluid–structure interaction (FSI) to evaluate their acoustic insulation.     

Stiffness control of low frequency acoustic transmission through the walls of rectangular ducts

An investigation is reported here on the use of “stiffness control” to reduce low frequency acoustic “breakout” through the walls of rectangular air-moving ducts; in this, attempts are made to increase the fundamental transverse resonance frequency of the duct walls (by using materials with a high stiffness/mass ratio) so that the capacitive (stiffness) controlled nature of the wall impedance below this frequency may be exploited to raise the wall transmission loss and remove low frequency resonances. Some degree of success is achieved in this, and the results appear encouraging. As a necessary part of the work, the nature of the acoustic/structural wave combinations is explored in more detail than hitherto, and a simplified low frequency approximate method of determining the transmission loss of ducts is also given.     

基于电磁力近似算法的驱动电机NVH快速仿真方法

电动汽车驱动电机产生的电磁噪声是汽车NVH关注的重点问题,对其进行全转速段多工况NVH仿真通常需要耗费大量时间和计算资源。该文通过有限单元分析揭示了电机气隙电磁力随转速变化的规律,并根据这一规律提出了基于外特性曲线的电磁力时间缩放及插值的近似算法。文章采用电磁力到结构网格的映射算法对结构振动有限元模型进行激励力加载,使用声场有限元方法计算电机的辐射噪声,最终实现了车用驱动电机的电磁振动及噪声的快速仿真。使用该方法对车用电机进行全转速段振动噪声仿真,可大大压缩多工况电磁场有限元分析所需的计算时间,提升仿真效率。     

A finite element model for laser-induced leaky waves at fluid–solid interfaces

The finite element method is firstly used to simulate the laser-induced leaky waves at fluid–solid interfaces. Corresponding models and arithmetic are developed, in that the fluid–solid interactions are described by a coupling matrix and the infinite boundary of fluid domain is modeled by acoustic absorption elements. Typical calculations are executed for air–aluminum plane and cylindrical interfaces. The results are in very good agreements with the experimental signals in available literatures, which verify the correctness of our finite element model for simulating laser-induced leaky wave at fluid–solid interfaces. And some elementary conclusions are obtained for the laser induced leaky waves.     

A FINITE ELEMENT FORMULATION FOR COUPLING RIGID AND FLEXIBLE BODY DYNAMICS OF ROTATING BEAMS

The work presented in this paper is based on an existing comprehensive formulation for rotating flexible systems. In the existing formulation the flexible degrees of freedom (d.o.f.) are represented by an analytically computed modal basis and the coupling matrices between the rigid- and the flexible-body d.o.f. are developed based on the analytical modal representation of the flexible d.o.f. In this paper, the existing formulation is generalized for rotating beams by representing the flexible d.o.f. either as physical d.o.f. of a finite element formulation or as a set of retained and internal d.o.f. of a Craig-Bampton formulation. The coupling matrices between the rigid-body rotation and the flexible d.o.f. are developed accordingly. The non-linear effects from the work done by the centrifugal forces are included in the formulation. Finite element shape functions of a beam element in a three-dimensional space and finite element shape functions for solid elements are employed for deriving the coupling terms between the rigid-body d.o.f. and the physical d.o.f. An additional transformation is required and performed when the right-body d.o.f. are coupled with the internal and the retained d.o.f. of a Craig-Bampton formulation. The coupled system of equations is solved in the time domain by combining the Newmark method for time integration and the Newton-Raphson method for solving the non-linear system of equations within each time step. Analyses are performed for a flexible rotating beam in order to validate the development. An analytical solution is compared with the new formulations that represent the rotating beam flexibility with the physical d.o.f. of beam or solid elements. The analytical solution is also compared to the formulation that represents the flexible d.o.f. in terms of retained and internal d.o.f. of a Craig-Bampton formulation. Very good correlation between the analytical and numerical results is observed.     

Numerical analysis of immersed finite cylindrical shells using a coupled BEM/FEM and spatial spectrum approach

This study numerically analyzes submerged cylindrical shells using a coupled boundary element method (BEM) with finite element method (FEM) in conjunction with the wave number theory, in which the spatial Fourier transform of surface velocity for cylinders is directly related to pressure in a far field. The acoustic loading is formulated using a symmetric complex matrix derived from a boundary integral equation where the symmetry is based on an acoustic reciprocal principle for surface acoustics. In this formulation the acoustic loading matrix is a large acoustic element whose degree of freedom is connected to the normal displacement of the vibrating structures. The coupled BEM/FEM equation is a banded, symmetric matrix, and thus its bandwidth can be minimized using a proper algorithm. This formulation significantly increases numerical efficiency. The computed normal velocity is thus transformed to wave number representation to examine acoustic radiation. A finite plane cylindrical shell, without attached stiffeners, and a shell with internal ring stiffeners are chosen to demonstrate the present analysis procedure. The far field pressure computed directly from the integral equation and predicted by wave number theory correlates closely with increasing vibrating frequency. Meanwhile, the influences of the internal ring structures on acoustic radiation are examined using the wave number theory, which helps in understanding how internal structures influence radiated noise.     

Acoustic modelling of exhaust devices with nonconforming finite element meshes and transfer matrices

Transfer matrices are commonly considered in the numerical modelling of the acoustic behaviour associated with exhaust devices in the breathing system of internal combustion engines, such as catalytic converters, particulate filters, perforated mufflers and charge air coolers. In a multidimensional finite element approach, a transfer matrix provides a relationship between the acoustic fields of the nodes located at both sides of a particular region. This approach can be useful, for example, when one-dimensional propagation takes place within the region substituted by the transfer matrix. As shown in recent investigations, the sound attenuation of catalytic converters can be properly predicted if the monolith is replaced by a plane wave four-pole matrix. The finite element discretization is retained for the inlet/outlet and tapered ducts, where multidimensional acoustic fields can exist. In this case, only plane waves are present within the capillary ducts, and three-dimensional propagation is possible in the rest of the catalyst subcomponents. Also, in the acoustic modelling of perforated mufflers using the finite element method, the central passage can be replaced by a transfer matrix relating the pressure difference between both sides of the perforated surface with the acoustic velocity through the perforations. The approaches in the literature that accommodate transfer matrices and finite element models consider conforming meshes at connecting interfaces, therefore leading to a straightforward evaluation of the coupling integrals. With a view to gaining flexibility during the mesh generation process, it is worth developing a more general procedure. This has to be valid for the connection of acoustic subdomains by transfer matrices when the discretizations are nonconforming at the connecting interfaces. In this work, an integration algorithm similar to those considered in the mortar finite element method, is implemented for nonmatching grids in combination with acoustic transfer matrices. A number of numerical test problems related to some relevant exhaust devices are then presented to assess the accuracy and convergence performance of the proposed procedure.