The spatial distribution of sound pressure within scaled replicas of the human ear canal

A theoretical model for calculating the variation of sound pressure within the ear canal is presented. The theory is an extension of the horn equation approach, and accounts for the variation of cross-sectional area and curvature of the ear canal along its length. Absorption of acoustic energy at the eardrum is included empirically through an effective eardrum impedance that acts at a single location in the canal. For comparison, measurements of the distribution of sound pressure have been made in two replica ear canals. Both replicas have geometries that duplicate, as nearly as possible, that of a real human ear canal, except that they have been scaled up in size to increase the precision of measurements. One of the replicas explicitly contains a load impedance to provide acoustical absorption at a single eardrum position. Agreement between theory and experiment was good. It is clear that at higher frequencies (above about 6 kHz in human ear canals), this theoretical approach is preferable to the more usual "uniform cylinder" approximation for the ear canal. At higher frequencies, there is no unique eardrum pressure; rather, very large variations of sound pressure are found over the tympanic membrane surface.     

Fast and highly accurate boundary element method for scattering calculation of defective gratings

A numerical scattering calculation method for defective gratings is proposed. This method is based on an integral equation method that computes a difference-field distribution, which is the difference between the scattering fields with and without the defect, and it is possible to simulate the arbitrary (finite) size and shape of a defect in the grating without any limitation. A calculation example is also presented to demonstrate the fast convergence and high accuracy of this method.     

Fast multipole accelerated boundary element method for the Helmholtz equation in acoustic scattering problems

We apply the fast multipole method (FMM) accelerated boundary element method (BEM) for the three-dimensional (3D) Helmholtz equation, and as a result, large-scale acoustic scattering problems involving 400000 elements are solved efficiently. This is an extension of the fast multipole BEM for two-dimensional (2D) acoustic problems developed by authors recently. Some new improvements are obtained. In this new technique, the improved Burton-Miller formulation is employed to over-come non-uniqueness difficultie...     

The use of the boundary element method in solving the problems of sound scattering by an elastic noncircular cylinder

A semianalytic solution of the problem of sound scattering by an elastic cylinder with a noncircular cross section is proposed. The problem is solved by the analytic-numerical boundary element method in terms of the ideal fluid theory and the linear theory of elasticity.     

Model and estimation method for predicting the sound radiated by a horn loudspeaker - With application to a car horn

This paper deals with a new car horn device made of a sound synthesizer and an electrodynamic horn loudspeaker. It presents an one-dimensional model allowing to predict the loudspeaker efficiency and a specific method to estimate experimentally the model parameters. First, this model aims at reducing the time spent in the design process. Second it aims at correcting the sound emitted by the sound synthesizer in order that the listener hears the sound designed for creating the warning message. The study gives a survey of the vast loudspeaker literature. It is based on the conventional electroacoustic approach used for electrodynamic loudspeakers and on wave propagation models used for characterizing acoustic horns. The estimation of the model parameter values is performed using measurements of the electrical impedance of the loudspeaker and of the acoustic impedance of the horn. The model is assessed by comparing the calculated and measured electrical impedances and horn efficiencies. Results show that the model predicts well the horn efficiency up to 2500 Hz, the limitation being due to the horn radiation impedance modelization.     

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.     

边界积分方程法求解目标的声散射T矩阵

提出了计算任意表面形状刚性边界目标散射的基于边界积分方程的T矩阵方法(TMM-BIE).利用Helmholtz积分方程法(HIEM)计算目标表面声场,替代扩展边界法(EBCM)计算中对目标表面声场的近似处理,解决了扩展边界法不能计算任意形状目标的散射T矩阵问题.文中计算了刚性边界的球目标、有限长圆柱目标以及非对称的三维散射体-猫眼(cat's-eye)模型的散射指向性和T矩阵.通过与解析解和HIEM结果比较,证明该方法的有效性.     

A method for multi-frequency calculation of boundary integral equation in acoustics based on series expansion

The paper presents a method to solve the problem of multi-frequency calculation of Helmholtz boundary integral equation in acoustics. Based on series expansion, system matrices are independent of wavenumber and become the matrix power series of wavenumber. As a result, all matrices in the matrix power series are only dependent on the structure geometry. In addition, an element transform method to calculate the singular integral and Cauchy singular integral is also discussed because the singular integral need to be solved using the method. The convergence of the series expansion method is also proved in this paper. The effectiveness of the method is confirmed by two numerical examples.     

小尺度阻尼边界封闭空间声传递函数的有限元素法计算

如何求解阻尼边界封闭空间中声源点到接收点的低频声传递函数已成为目前小尺度封闭空间可听化技术研究的关键技术，能处理任意形状及复杂边界条件的有限元素法可作为求解该问题的适合方法，以室内声声有源Helmholtz方程及其相应边界方程为基础，本文推导出了用于小尺度阻尼边界封闭空间声传递函数的有限元素求解方法，并编制了相应的计算机程序，在算例中，首先通过与模态叠加法计算结果进行比较，验证了该方法的正确性。最后计算了某型车体内腔中任意两点间声传递函数。     

Experiments on the solution of the helmholtz equation using the finite element method and a variational approach in the case of domains of complicated boundary shape

Domains of ‘exotic’ boundary shape are of interest in several technological applications—acoustic and electromagnetic waveguides, solid propellant rocket cross-sections, printed circuit boards, etc.The present paper describes some experiments performed to determine the eigenvalues of a vibrating, ideal membrane.It is shown that the finite element method yields results which are in very good agreement with values determined by means of an analytical approach in the case of a membrane of a cardioidal shape.     

室内声场无网格数值算法性能影响因素分析

基于室内无网格数值算法的理论和实验研究,本文进一步利用控制变量法,结合计算效率对影响计算精度的因素进行了全面分析,包括节点、高斯点的分布方式及其密度,以及构造无网格形函数过程中的基函数类型、权函数类型,并通过对一类基准问题的大量数据实验获得了适用于小尺度封闭空间的最佳支持域半径范围。基于有关结论对一个实际机舱进行了建模分析,将声压级计算值与测量值对比,验证了这些结论的正确性。     

A boundary element method for the calculation of noise barrier insertion loss in the presence of atmospheric turbulence

Atmospheric turbulence is an important factor that limits the amount of attenuation a barrier can provide in the outdoor environment. It is therefore important to develop a reliable method to predict its effect on barrier performance. The boundary element method (BEM) has been shown to be a very effective technique for predicting barrier insertion loss in the absence of turbulence. This paper develops a simple and efficient modification of the BEM formulation to predict the insertion loss of a barrier in the presence of atmospheric turbulence. The modification is based on two alternative methods: (1) random realisations of log-amplitude and phase fluctuations of boundary sources and (2) de-correlation of source coherence using the mutual coherence function (MCF). An investigation into the behaviours of these two methods is carried out and simplified forms of the methods developed. Some systematic differences between the predictions from the methods are found. When incorporated into the BEM formulation, the method of random realisations and the method of MCF de-correlation provide predictions that agree well with predictions by the parabolic equation method and by the scattering cross-section method on a variety of thin barrier configurations.     

Assessing the effect of a barrier between two rooms subjected to low frequency sound using the boundary element method

The boundary element method (BEM) has been used to compute the acoustic wave propagation through a single vertical panel, which separates two rooms, made of concrete, when one of the rooms is excited by a steady-state, spatially sinusoidal, harmonic line load pressure at low frequencies. This work focuses on how the connection of the panel to the ceiling affects the acoustic insulation provided by the wall. Perfect double-fixed partitions and acoustic barrier-type structures with differently-sized gaps between the ceiling and the barrier are studied. The BEM model is formulated in the frequency domain and takes the air-solid interaction fully into account. Insulation dips are localised in the frequency domain and identified with dips associated with both the wall's natural dynamic vibration modes and with those associated with the air in the rooms. The influence of the wall's thickness on acoustic insulation is also analysed. The computed results obtained with the acoustic barrier type structure are compared with those obtained by a rigid model. The importance of the rooms' surface conditions is assessed, modelling the rooms with cork.     

A basic study on the sound field analysis of periodic structures by boundary integral equation method

This study deals with the development of the approximate method to analyze the sound field around equally spaced finite obstacles, using the periodic boundary condition. First, on the assumption that the equally spaced finite obstacles are the periodically arranged obstacles, the sound field is analyzed by boundary integral equation method with a Green’s function which satisfies the periodic boundary condition. Furthermore, by comparing these results and the exact solution by using the fundamental solution as Green’s function, the validity of the approximate method is also investigated. Next, in order to evaluate the applicability of the approximate method, the simple formula using some parameters, i.e., the frequency, the period, and the number of obstacles, etc., is proposed. The results of the sound field analysis applied the formula are presented.     

小尺度封闭空间声场的无网格数值算法

无网格法是一种新兴的数值计算方法,具有不需要网格支持的特点。本文将该方法引入室内声学建模,推导了无网格声场数值计算模型,并将其应用于典型小尺度封闭空间内部声场的数值分析。针对声传递函数,将本方法与理论解和SYSNOISE计算结果进行了比较,并将计算的混响时间与实验测量结果作了对比,表明本方法具有良好的精度。     

Effects of normal and pathologic eardrum impedance on sound pressure in the aided ear canal: a computer simulation

Reported herein are results of computer simulations of aided sound spectra in ears with normal and pathologic eardrum impedance. The computer technique used in this study has been reported elsewhere [D. P. Egolf, D. R. Tree, and L. L. Feth, J. Acoust. Soc. Am. 63, 264-271 (1978)]. Consequently, to develop reader confidence in the computer scheme, its application to real ears was first tested. This was accomplished by (1) comparing computed spectral data with in-the-ear measurements and (2) comparing real ear minus 2-cc coupler data-both computer generated--with an idealized difference curve published elsewhere [R. M. Sachs and M. D. Burkhard, unpublished rep. no. 20022-1, Industrial Research Products, Inc., Elk Grove Village, IL (1972)]. Results indicate that the wide variation in eardrum impedance among normals evidenced in other studies produces a corresponding wide variation in aided spectrum shape. Likewise, simulations utilizing two sets of pathologic eardrum impedance data obtained from the literature show that aided sound spectra in such ears are likely to be significantly different from those occurring in normal ears. These findings suggest, as others have concluded, that there may be a substantial variation in spectrum shape among individuals wearing identically the same hearing aid--even if those individuals have normal hearing. In conclusion, questions are raised about the use of real-ear simulators and the need for a comprehensive computer-based model of an entire hearing aid.     

有限元+边界元——修正的模态分解法预报水下旋转薄壳的振动和声辐射

本文提出了一种有限元+边界元——修正的模态分解法用于预报水下结构的振动和声辐射问题.通过引入结构的剩余模态计入被忽略的高阶模态的准静态响应,使模态分解法的收敛性大大改善.文中以轴对称力作用下水下弹性薄球壳振动和声辐射问题为例进行了数值计算,给出了ka=1,2,3和4时球壳表面位移、声压和远场辐射声的计算结果.与原有的方法比较可见,该方法提高了模态分解法的收敛性,特别对远场辐射声指向性尤为明显。