Burton-Miller改进型边界方程的多频计算方法

提出了一种采用Burton-Miller改进型边界积分方程进行多频计算的方法。将Burton-Miller方程中的高奇异积分转化为弱奇异积分形式,获得Burton-Miller改进型边界积分方程;将方程中格林函数进行Taylor级数展开,并把波数从方程中分离出来,从而使随波数变化的计算矩阵表示为波数的矩阵级数形式。数值分析表明,本方法不仅保证了解在全波数范围内的唯一性,并且计算频率点数较多时可以节约大量时间,提高计算效率。     

三维声学多层快速多极子边界元及其应用

快速多极子边界元算法可以加速矩阵和向量乘法运算, 将传统边界元算法的计算量和内存占用量分别降为O(N log²N)和O(N), 适用于大型声学模型模拟计算. 本文发展了一种基于Burton-Miller方程的三维多层声学快速多极子边界元算法. 将新的自适应树状算法应用到对角形式的快速多极子边界元算法, 并使用最新提出的解析式源点矩计算公式, 进一步提高了快速多极子边界元的计算效率. 绝对软球体在内部共振频率处的散射声场计算, 验证了所发展算法在共振频率处求解的正确性. 与Bapat所提供的程序在多脉动球体辐射声场计算精度的比较, 验证了算法及程序在大型模型声学计算中的准确性, 同时显示了其求解的高效性. 最后, 将该算法用于车内声场及水下声学探测的分析计算.     

子波谱方法在三维声辐射和声散射中的应用

将边界变量用二维子波展开,获得了三维任意边界条件声辐射和声散射的边界积分方程的子波谱方法。采用以子波为权函数的Gauss积分法计算子波谱方法的系数,获得了与传统边界元法相同的计算量,克服了普通积分法计算子波系数计算量大甚至难以收敛的缺点;采用Duffy的方法解决了子波谱方法中的奇异积分,使其能够用普通的Gauss积分法计算。算例表明:子波谱方法系数矩阵压缩率超过50%以后,计算精度仍然高于传统边界元方法。     

An improved series expansion method on the multi-frequency analysis of acoustic boundary element

For the multi-frequency acoustic analysis, a series expansion method has been introduced to reduce the computation time of the frequency-independent parts, but the Runge phenomenon will arise when this method is employed in high frequency band. Therefore, this method is improved by analyzing the application condition and proposing the selection principle of the series truncation number. The argument interval can be adjusted with the wavenumber factor. Therefore, the problem of unstable numeration and poor precision can be solved, and the application scope of this method is expanded. The numerical example of acoustic radiation shows that the improved method is correct for acoustic analysis in wider frequency band with less series truncation number and computation amount.     

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.     

边界元法循环平稳近场声全息理论研究

循环平稳声场是工程中经常遇到的一种特殊非平稳声场,声压信号受到调制作用,导致频谱出现边带现象,经典的近场声全息技术重建得到的声场无法反映声场的调制特性。在平面循环平稳近场声全息基础上,提出一种边界元法的循环平稳近场声全息技术,用二阶循环统计量理论代替传统的傅里叶分析,并以声压的循环谱密度取代其频谱及功率谱密度作为重建量,可用于循环平稳声场中具有复杂表面声源的辐射声场。由于循环谱密度对循环平稳信号具有解调功能,用该方法重建得到的循环谱密度能有效地反映调制和载波信号的信息。仿真分析与实验表明了本理论的有效性和精度能满足工程要求。     

Research on the cyclostationary nearfield acoustic holography based on boundary element method

Cyclostationary sound field is a special kind of nonstationary sound field, in which the pressure signal is modulated seriously and sidebands exist in its spectrum. The reconstructed sound field can＇t figure the cyclostationary features in conventional Nearfield Acoustic Holography （NAH） procedure. On the basis of planar cyclostationary NAH, the cyclostationary NAH based on boundary element method is proposed which can be utilized to analyze radiators with complicated surface. Replacing the Fourier＇s transform with the second-order cyclic statistics, the Cyclic Spectral Density （CSD） functions is used as the reconstructed physical quantity in the proposed NAH technique, instead of the spectrum or power spectral density of pressure signal. By virtue of the demodulation ability of CSD function, the reconstructed CSD can effectively express the information of modulating and carrier wave respectively. The simulation and experiment illustrate that the validity and accuracy of this cyclostationary NAH technique satisfy the request of engineering.     

Stabilization of time domain acoustic boundary element method for the interior problem with impedance boundary conditions

The time domain boundary element method (BEM) is associated with numerical instability that typically stems from the time marching scheme. In this work, a formulation of time domain BEM is derived to deal with all types of boundary conditions adopting a multi-input, multi-output, infinite impulse response structure. The fitted frequency domain impedance data are converted into a time domain expression as a form of an infinite impulse response filter, which can also invoke a modeling error. In the calculation, the response at each time step is projected onto the wave vector space of natural radiation modes, which can be obtained from the eigensolutions of the single iterative matrix. To stabilize the computation, unstable oscillatory modes are nullified, and the same decay rate is used for two nonoscillatory modes. As a test example, a transient sound field within a partially lined, parallelepiped box is used, within which a point source is excited by an octave band impulse. In comparison with the results of the inverse Fourier transform of a frequency domain BEM, the average of relative difference norm in the stabilized time response is found to be 4.4%.     

基于子空间投影的声辐射多频分析算法

针对边界元法在声辐射多频分析中的困难,提出了一种基于子空间投影的快速插值算法。该方法将所求解的声学量视为一个线性系统的传递函数,然后采用Krylov投影降阶方法的无矩阵形式对原系统进行模型降阶,并通过降阶系统的传递函数来实现对所求声学量的频率插值计算。文中分别采用等距频率插值和自适应插值方案,计算了三种模型算例的辐射声压和声功率。数值结果表明,本算法可以在保证一定计算精度的前提下,显著地提高声辐射多频分析的计算速度。     

Krylov subspace iterative methods for boundary element method based near-field acoustic holography

The reconstruction of the acoustic field for general surfaces is obtained from the solution of a matrix system that results from a boundary integral equation discretized using boundary element methods. The solution to the resultant matrix system is obtained using iterative regularization methods that counteract the effect of noise on the measurements. These methods will not require the calculation of the singular value decomposition, which can be expensive when the matrix system is considerably large. Krylov subspace methods are iterative methods that have the phenomena known as "semi-convergence," i.e., the optimal regularization solution is obtained after a few iterations. If the iteration is not stopped, the method converges to a solution that generally is totally corrupted by errors on the measurements. For these methods the number of iterations play the role of the regularization parameter. We will focus our attention to the study of the regularizing properties from the Krylov subspace methods like conjugate gradients, least squares QR and the recently proposed Hybrid method. A discussion and comparison of the available stopping rules will be included. A vibrating plate is considered as an example to validate our results.     

运动声源的边界元声全息识别方法研究

提出了一种可实现任意形状的运动结构噪声源识别的声全息方法。通过结合移动框架技术与边界元声全息技术两种算法的特点,提出利用移动框架技术将存在多普勒效应的时域数据转换成边界元声全息所需的双平面全息数据,然后由边界元法声全息公式重构任意结构表面的声学信息,实现运动结构噪声源定位。该方法既具有移动框架技术处理运动问题的快速简便,又具有边界元方法可处理任意形状问题的特点。最后在半消声水池中,对运动速度为9.96 cm/s的带帽圆柱壳体进行了试验验证,结果表明:在低速条件下,该方法能够准确反演得到该结构的表面有功声强以及声压等声场信息,从而实现噪声源定位。由于条件有限,高速验证需进一步验证。     

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...     

An approximate method to acoustic radiation problems: element radiation superposition method

An approximate method is brought forward to predict the acoustic pressure based on the surface velocity. It is named Element Radiation Superposition Method （ERSM）. The study finds that each element in Acoustic Transfer Vector （ATV） equals the acoustic pressure radiated by the corresponding surface element vibrating in unit velocity and other surface elements keep still, that is the acoustic pressure radiated by the corresponding baffled piston vibrating in unit velocity. So, it utilizes the acoustic pressure radiated by a baffled piston to establish the transfer relationship between the surface velocity and the acoustic pressure. The total acoustic pressure is obtained through summing up the products of the surface velocity and the transfer quantity. It adopts the regular baffle to fit the actual baffle in order to calculate the acoustic pressure radiated by the baffled piston. This approximate method has larger advantage in calculating speed and memory space than Boundary Element Method. Numerical simulations show that this approximate method is reasonable and feasible.