Prediction of sound level at high-frequency bands by means of a simplified boundary element method

A simplified boundary element method (BEM) for dealing with high-frequency sound is proposed. The boundary integral equation is modified into a quadratic form to enable the prediction of sound levels in the one-third octave band analysis. Monopole and dipole source terms in the conventional BEM are transformed into the auto- and cross-spectra of two vibrating sources, in which the cross-spectra are eventually neglected by assuming that the correlation coefficients involved are negligible. The present method is compared with the Rayleigh integral for calculating the sound pressure radiated from a baffled panel, in terms of the application limit. The characteristic length of the boundary element and the applicable frequency range can be determined by the lower limit value of the correlation coefficient. As a test example, the field pressure radiated from a partially vibrating sphere is predicted and the resultant trend is in good agreement with the analytic solution as far as the related correlation coefficient satisfies the assumption. The overdetermination process for overcoming nonuniqueness in exterior radiation problems is unnecessary in the present method because phase information can be ignored. The results of the calculation show that the proposed method is acceptable for solving the exterior radiation problem at a high-frequency range in a timely manner.     

基于联合波叠加法的浅海信道下圆柱壳声辐射研究

针对浅海信道下弹性结构声辐射预报尚无高效可靠的研究方法,提出了一种浅海信道下弹性结构声辐射快速预报的联合波叠加法.该方法结合了浅海信道传输函数、多物理场耦合数值计算法和波叠加法理论,运用该方法可对浅海信道下弹性结构辐射声场进行快速预报.经数值法和解析解法验证后,从信道下辐射源、环境影响和辐射声场测量的角度研究分析了浅海信道下弹性圆柱壳的声辐射特性,阐释了进行浅海信道下结构声辐射研究的必要性.研究结果表明,仅在低频浅海信道下弹性结构可近似等效为点源,信道上下边界对声场产生显著的耦合影响,高频段的空间声场指向性分布尤为明显,垂直线列阵进行信道下结构辐射声功率测量时,测量结果受到信道环境边界和潜深的影响较大.     

A computational method of evaluating noncompact sound based on vortex sound theory

A numerical investigation is made of the production of sound by turbulence interacting with a noncompact body. The problem is formulated in the frequency domain by extending the theory of vortex sound proposed by Howe. The anomalous "numerical" generation of sound by the sudden termination of Lighthill's stress tensor at the outer boundary of a finite computational domain is avoided by identification of "scattered" sound sources that generate sound principally by interaction with the solid surface. It is argued that the boundary element method is the most efficient means of computing the aeroacoustic Green's function for the problem, because it requires a minimum of CPU time, is not prone to numerical errors such as dispersion and dissipation during propagation, and the radiation condition is easily applied at the outer boundary. The method is applied to the problem of sound generation by high Reynolds number flow past a circular cylinder. The "scattered" sources are shown to be confined to the vicinity of the cylinder surface. At low frequencies the radiation has a dipole-like directivity in agreement with the compact approximation. However, the directivity is quite different at high frequencies, where our noncompact method predicts a more complicated "leaf-like" radiation pattern.     

Efficient calculation of two-dimensional periodic and waveguide acoustic Green's functions

New representations and efficient calculation methods are derived for the problem of propagation from an infinite regularly spaced array of coherent line sources above a homogeneous impedance plane, and for the Green's function for sound propagation in the canyon formed by two infinitely high, parallel rigid or sound soft walls and an impedance ground surface. The infinite sum of source contributions is replaced by a finite sum and the remainder is expressed as a Laplace-type integral. A pole subtraction technique is used to remove poles in the integrand which lie near the path of integration, obtaining a smooth integrand, more suitable for numerical integration, and a specific numerical integration method is proposed. Numerical experiments show highly accurate results across the frequency spectrum for a range of ground surface types. It is expected that the methods proposed will prove useful in boundary element modeling of noise propagation in canyon streets and in ducts, and for problems of scattering by periodic surfaces.     

On the modeling of narrow gaps using the standard boundary element method

Numerical methods based on the Helmholtz integral equation are well suited for solving acoustic scattering and diffraction problems at relatively low frequencies. However, it is well known that the standard method becomes degenerate if the objects that disturb the sound field are very thin. This paper makes use of a standard axisymmetric Helmholtz integral equation formulation and its boundary element method (BEM) implementation to study the behavior of the method on two test cases: a thin rigid disk of variable thickness and two rigid cylinders separated by a gap of variable width. Both problems give rise to the same kind of degeneracy in the method, and modified formulations have been proposed to overcome this difficulty. However, such techniques are better suited for the so-called thin-body problem than for the reciprocal narrow-gap problem, and only the first is usually dealt with in the literature. A simple integration technique that can extend the range of thicknesses/widths tractable by the otherwise unmodified standard formulation is presented and tested. This technique is valid for both cases. The modeling of acoustic transducers like sound intensity probes and condenser microphones has motivated this work, although the proposed technique has a wider range of applications.     

Phased Array Beam Fields of Nonlinear Rayleigh Surface Waves

This study concerns calculation of phased array beam fields of the nonlinear Rayleigh surface waves based on the integral solutions for a nonparaxial wave equation.Since the parabolic approximation model for describing the nonlinear Rayleigh waves has certain limitations in modeling the sound beam fields of phased arrays,a more general model equation and integral forms of quasilinear solutions are introduced.Some features of steered and focused beam Gelds radiated from a linear phased array of the second harmonic Rayleigh wave are presented.     

A Chebyshev–Lagrangian method for acoustic analysis of a rectangular cavity with arbitrary impedance walls

A general Chebyshev–Lagrangian method is proposed to obtain the analytical solution for a rectangular acoustic cavity with arbitrary impedance boundary conditions. The originality of the present paper is the successful attempt of applying orthogonal polynomials, such as Chebyshev polynomials of the first kind, to the analysis of a rectangular sound field with general wall impedance. The sound pressure is uniformly expressed as triplicate Chebyshev polynomial series which is independent in each direction. The Chebyshev polynomial series solution is obtained using the Rayleigh–Ritz procedure after considering the influence of boundary impedance on the cavity as the work done by the impedance surfaces in the Lagrangian function. The accuracy and reliability of the proposed method are validated against the analytical solutions and some numerical results available in the literature. Excellent orthogonality and complete properties of the Chebyshev polynomials ensure the rapid convergence, numerical stability, high accuracy of the current solution. The simplicity and low computational cost of the present approach make it preferable to obtain the results of complex models even in the relative high frequency range by choosing enough truncated terms in the sound pressure expression. Numerous cases with various uniform or non-uniform impedance boundary conditions are analyzed numerically and some of the results can be used as benchmark. It is shown that the impedance boundary condition can effectively influence or modify the acoustic characteristics and response of a cavity.     

基于瑞利积分叠加法的聚焦换能器声场特性研究

基于经典的瑞利积分,提出考虑非线性传播、各次谐波衰减的声场瑞利积分线性叠加算法.分析其原理,并以凹球面聚焦换能器为例,采用该算法研究媒质衰减和非线性传播特性影响声焦域的规律.并与Khokhov-Zabolotskaya-Kuznesov(KZK)数值算法,以及实验结果进行比较,验证瑞利积分线性叠加算法描述高强度聚焦超声(HIFU)声场的有效性.     

A direct mixed-body boundary element method for packed silencers

Bulk-reacting sound absorbing materials are often used in packed silencers to reduce broadband noise. A bulk-reacting material is characterized by a complex mean density and a complex speed of sound. These two material properties can be measured by the two-cavity method or calculated by empirical formulas. Modeling the entire silencer domain with a bulk-reacting lining will involve two different acoustic media, air and the bulk-reacting material. Traditionally, the interior silencer domain is divided into different zones and a multi-domain boundary element method (BEM) may be applied to solve the problem. However, defining different zones and matching the elements along each interface is tedious, especially when the zones are intricately connected. In this paper, a direct mixed-body boundary element method is used to model a packed silencer without subdividing it into different zones. This is achieved by summing up all the integral equations in different zones and then adding the hypersingular integral equations at interfaces. Several test cases, including a packed expansion chamber with and without an absorbing center bullet, and a parallel baffle silencer, are studied. Numerical results for the prediction of transmission loss (TL) are compared to experimental data.     

Prediction of Outdoor Noise Propagation Induced By Single-Phase Power Transformers

Outdoor power transformers are one of the most pervasive noise sources in power transmission and distribution systems. Accurate prediction of outdoor noise propagation plays a dominant role for the evaluation and control of noise relevant to the transformer stations. In this paper surface vibration tests are carried out on a scale model of a single-phase transformer tank wall at different excitation frequencies. The phase and amplitude of test data are found to be randomly distributed when the excitation frequency exceeds the seventh mode frequency, which allows the single-phase power transformer to be simplified as incoherent point sources. An outdoor-coherent model is subsequently developed and incorporated with the image source method to investigate noise propagation from single-phase power transformers, due to the occurrence of multiple reflections and diffractions in the propagation path of each point source. The proposed model is used to calculate the sound field of the power transformer group by exploiting the additional phase information. In comparison with the ISO9613 model and the boundary element method, it is found that the proposed coherent image source method leads to more accurate prediction results, and hence better performance for the prediction of the outdoor noise induced by single-phase power transformers.     

Structural topology optimization on sound radiation at resonance frequencies in thermal environments

Thermal and acoustic environments pose severe challenges to the structural design of hypersonic vehicles.One of them is to find optimal design that exhibits ideal acoustic characteristics in a frequency band,which is discussed in this paper through topology optimization aiming at resonance sound radiation in thermal environments.The sound radiation at resonance frequencies is the main component of response,minimization on which is likely to provide a satisfactory design.A bi-material plate subjected to uniform temperature rise and excited by harmonic loading is studied here.Thermal stress is first evaluated and considered as prestress in the following dynamic analysis;radiated sound power is then calculated through Rayleigh integral.Sensitivity analysis is carried out through adjoint method considering the complicated relationship between stress-induced geometric stiffness and design variables.As the resonance frequency is constantly changing during the optimization,its sensitivity should be considered.It is also noticed that mode switching may occur,so mode tracking technique is employed in this work.Some numerical examples are finally discussed.     

三维浅海下弹性结构声辐射预报的有限元-抛物方程法

利用多物理场耦合有限元法对结构和流体适应性强、抛物方程声场计算高效准确的特点,提出了三维浅海波导下弹性结构声振特性研究的有限元-抛物方程法.该方法采用多物理场耦合有限元理论建立浅海下结构近场声辐射模型,计算局域波导下结构声振信息,并提取深度方向上复声压值作为抛物方程初始值;然后采用隐式差分法求解抛物方程以步进计算结构辐射声场.重点介绍了该方法对浅海下结构声辐射计算的准确性、高效性以及快速收敛性后,对Pekeris波导中有限长弹性圆柱壳的声振特性进行了分析.研究得出,当圆柱壳靠近海面(海底)时,其耦合频率比自由场下的要高(低),当潜深达到一定范围时,与自由场耦合频率基本趋于一致;在低频远场,结构辐射场与同强度点源声场具有一定的等效性,且等效距离随着频率增加而增加;由于辐射声场受结构振动模态、几何尺寸和简正波模式影响,结构辐射场传播的衰减规律按近场声影响区、球面波衰减区、介于球面波和柱面波衰减区、柱面波衰减区四个扩展区依次进行.     

短圆管换能器辐射阻抗

辐射阻抗是换能器最重要的辐射声场特性参数之一,影响着换能器的谐振频率、频带宽度、效率以及辐射声功率等.随着圆管换能器半径和高度的不断变化,想直接得到声场瑞利积分的解析解是十分困难的.该文通过建立经验公式模型来解决此问题.首先,通过有限元软件计算圆管换能器辐射阻抗的数值解.然后利用MATLAB工具进行曲线拟合.经过反复逼...     

Sound field separating on arbitrary surfaces enclosing a sound scatterer based on combined integral equations

To eliminate the limitations of the conventional sound field separation methods which are only applicable to regular surfaces, a sound field separation method based on combined integral equations is proposed to separate sound fields directly in the spatial domain. In virtue of the Helmholtz integral equations for the incident and scattering fields outside a sound scatterer, combined integral equations are derived for sound field separation, which build the quantitative relationship between the sound fields on two arbitrary separation surfaces enclosing the sound scatterer. Through boundary element discretization of the two surfaces, corresponding systems of linear equations are obtained for practical application. Numerical simulations are performed for sound field separation on different shaped surfaces. The influences induced by the aspect ratio of the separation surfaces and the signal noise in the measurement data are also investigated. The separated incident and scattering sound fields agree well with the original corresponding fields described by analytical expressions, which validates the effectiveness and accuracy of the combined integral equations based separation method.     

An analytical model to estimate the performance of an indoor barrier at low-medium frequencies

Indoor barriers are now widely used for sound insulation. This paper examines the performance of indoor barriers in the low-medium frequency range and analyses the interaction between different natural modes of a room-barrier-room system. Morse proposed a theoretical model to calculate the sound field in a coupled-room, but this model neglects the surface integral of the boundary values of sound pressure. To estimate the performance of a barrier in an indoor environment, an analytical model is proposed that modifies the Green’s function for a non-rigid boundary enclosure and approximates the surface integral by a pre-estimated sound pressure based on Morse’s model. An additional approximation has been made in the proposed model to neglect the coupling area in the calculation of the surface integral. The proposed model used to predict the insertion loss of the barrier is verified by the experimental results using a 1:5 scale model. The predicted results agree well with the measured results at lower frequencies.     

Rayleigh wave at the boundary of an inhomogeneous nonlinear viscoelastic half-space

In the approximation of weak nonlinearity and weak viscosity of the medium, we obtain an equation describing the spectral density of the particle horizontal velocity for a Rayleigh wave propagating along the boundary of a half-space. The coefficients of nonlinear interaction between the wave harmonics are found on the assumption that the third-order elastic moduli arbitrarily depend on the depth. We find expressions for the complex correction to the wave frequency due to small relaxation corrections to the elastic moduli and small variations in the medium density, which arbitrarily depend on the depth as well. The imaginary part of this correction to the frequency determines the decay of the linear Rayleigh wave due to small relaxation corrections to the elastic moduli arbitrarily dependent on the depth. Using numerical simulation (with allowance for the interaction of 500 harmonics), we study distortions of an initially harmonic Rayleigh wave for a particular dependence of variations in the nonlinear moduli on the depth. An integral equation is derived for the nonlinear elastic moduli as functions of the depth. It is shown that for independent spatio-temporal distributions of the viscous moduli, functions determining the dependence of the viscosity on the depth are described by an analogous integral equation. __________ Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 50, No. 3, pp. 212–226, March 2007.     

透射边界条件在点声源海底地震波数值计算中的应用

航行舰船在海底岩土层中引起的弹性波被称为舰船地震波,主要由舰船低频辐射噪声引起,可用于识别舰船目标。本文采用大型有限元软件ANSYS中的流固耦合计算模块,结合多次透射公式(MTF)人工边界条件,对较为简单的水平分层海洋环境下低频点声源海底地震波进行了数值计算,并为了分析数值计算方法的精度,将数值计算结果与波数积分方法结果进行了比较。频率较低时两种方法的声传播损失曲线符合较好,频率较高时结果存在一定差别;两种计算方法所得声传播频率特性曲线的形式有所不同,但曲线总体变化趋势基本一致;而海底表面竖直位移、水平位移、竖直加速度和水平加速度的频率特性曲线基本符合。由此认为,基于多次透射公式人工边界,采用大型有限元软件ANSYS中的流固耦合模块,对较复杂环境下低频点声源海底地震波问题进行数值计算是基本可行的。     

Diffraction of spherical waves at an annular aperture in the use of the boundary diffraction wave theory: A comparison of different diffraction integral approaches

The integral expression for divergent spherical waves diffracted at an annular aperture is derived based on the theory of the boundary diffraction wave. The expressions for divergent spherical waves diffracted at a circular aperture and a disk, and the axial field are treated as the special cases of our general one. Numerical calculation results for axial and transversal intensity distributions are given to compare our results with the Kirchhoff diffraction integral, first and second Rayleigh diffraction integrals. As expected, our results are in agreement with those in the use of the Kirchhoff diffraction integral, but the computer time is reduced greatly by using the boundary diffraction wave theory. The four diffraction formulae are shown to be consistent for axial and transversal intensity distributions, if the source and observation points are positioned equally from the aperture, or the observation point is located enough far from the aperture. Otherwise, the mean value of the first and second Rayleigh diffraction integrals is equal to the result of the boundary diffraction wave theory.     

Sound propagation above an inhomogeneous plane: Boundary integral equation methods

A boundary integral equation method is used to compute the sound pressure emitted by a harmonic source above an inhomogeneous plane. First, the theoretical aspects of the problem (behaviour of the pressure around the discontinuities,…) are studied. Then, a comparison between theoretical levels and experimental levels obtained in an anechoic room is presented. It shows that the boundary integral equation (BIE) method is quite convenient for solving this kind of problem. Two interesting results are pointed out: (i) if only a prediction of maximum sound levels is needed, the attenuation is the same for a cylindrical source, a spherical source and N spherical sources, and so it is possible to transform some three-dimensional problems into two-dimensional ones; (ii) a numerical method of computation of the sound field above an inhomogeneous plane does not provide a correct prediction if each part of the plane is not accurately described by the boundary condition chosen.     

Single frequency sound propagation in flat waveguides with locally reactive impedance boundaries

A coherent image source method is presented for evaluating single frequency sound propagation from a point source in a flat waveguide with two infinite and parallel locally reactive boundaries. The method starts from formulating reflections of the spherical sound radiation into integrals of plane wave expansion, and the analytical evaluation of the integrals is simplified by introducing a physically plausible assumption that wave front shapes remain the same before and after each reflection on a reflective boundary. The proposed model can determine coherently the sound fields at arbitrary receiver locations in a flat waveguide, even when one boundary is highly sound absorptive. Being compared with the classical wave theory and the existing coherent ray-based methods, it is shown that the proposed method provides considerable accuracy and advantages to predict sound propagation in flat waveguides with a sound absorptive ceiling and a reflective floor over a broad frequency range, particularly at large distances from the source where the existing methods are problematic.