Predict acoustic field of vibrating beams by Helmholtz integral equation and BEM

New method of predicting the acoustic field radiation of vibratingbodies is presented.It is based on the Helmholtz integral equation and bounda-ry element method and applicable to the use of computers.The acoustic field ofthe cantilever beams has been calculated and measured.Test results haveproved the effectiveness of the predicting method.     

Structural-acoustic coupling in complex shaped cavities

Structural-acoustic interaction is a topic of increasing interest in the study of vehicle noise control. During recent years particular attention has been devoted towards analytical and numerical methods for the analysis of acoustic problems of complex shaped cavities. Among them non-local methods are very appropriate for the low and medium frequency range. The integral formulation of the Helmholtz equation allows the sound pressure level, radiated by a vibrating panel, to be determined. The method may be used to account for the acoustic structural coupling and can be straightforwardly extended to consider interconnected cavities, internal vibrating panels, internal barriers and absorbing materials. Comparisons with experimental results as well as with modal methods are presented which show satisfactory agreement.     

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.     

Coupled FEM/BEM for control of noise radiation and sound transmission using piezoelectric shunt damping

In this paper, we present a coupled finite element/boundary element method (FEM/BEM) for control of noise radiation and sound transmission of vibrating structure by passive piezoelectric techniques. The system consists of an elastic structure (with surface mounted piezoelectric patches) coupled to external/internal acoustic domains. The passive shunt damping strategy is employed for vibration attenuation in the low frequency range. The originality of the present paper lies in evaluating the classically used FEM/BEM methods for structural–acoustics problems when taking account smart systems at the fluid–structure interfaces.     

FEM calculation of an acoustic field in a sonochemical reactor

The spatial distribution of the acoustic amplitude in a sonochemical reactor has been numerically calculated using the finite element method (FEM). In the FEM program, the acoustic field in a sonochemical reactor is coupled with the vibration of the reactor's wall. The present calculations have revealed that the thin (thick) glass or stainless steel wall is nearly a free (rigid) boundary and that the glass wall is freer than the stainless steel wall. The influence of the attenuation coefficient of ultrasound on the acoustic field has also been studied in order to see the effect of bubbles on the acoustic field. As the attenuation coefficient increases, the vibration amplitude of the reactor's wall becomes smaller and the acoustic emission from the vibrating wall becomes weaker. The qualitative feature of the spatial pattern of sonochemiluminescence from an aqueous luminol solution has been reproduced by the calculation when the attenuation coefficient is in the range of 0.5-5m(-1). When the attenuation coefficient is less than about 0.05 m(-1), the standing wave pattern of an acoustic field in the liquid is very complex due to the acoustic emission from the vibrating wall. The present calculations have also revealed that some stripes of pressure antinodes have also been disconnected when the radius of the transducer is much smaller than the side length of the vibrating plate. The dependence of the acoustic field on the liquid height is also discussed.     

阶梯圆盘的设计及其声参数计算

由薄圆盘改进而来的阶梯型薄圆盘声波辐射器在空气中有着很好的应用,但由于阶梯的存在,需要根据在节线处位移连续、位移斜率连续、剪切力连续以及弯矩连续,加之其边界条件才能推导出频率方程。多一条节线,则多四个方程。变量多,方程系数复杂,频率方程难解。本文以单节线阶梯圆盘为例,提出了一种数值计算方法,编制了计算程序。计算结果与实验测试值符合较好。更进一步,可计算得到阶梯盘的声场分布、辐射阻抗等声学特性。本文为阶梯圆盘的设计和其声学性能的计算提供了一种方法。      

小阻尼界面房间声传输函数和声脉冲响应函数的有限元素法

有限元法可用于以声波动方程为基础通过数值计算求解室内声场,适用于分析界面阻抗非均匀分布和复杂形状房间内声场的低频特性。本文首先介绍了小阻尼界面条件下室内声场简正方式、声衰变系数、混响时间的ＦＥＭ计算方法。在此基础上导出了房间内两点之间声传输函数和声脉冲响应函数的ＦＥＭ计算模型,并以矩形房间为例详细讨论了有关细节。本文所讨论的计算模型可以映房间内不同的声源点,接收点位置上的声压频谱特性和脉冲响应的时     

A study on the applications of the acoustic design sensitivity analysis of vibrating bodies

The determination of the sensitivity of the acoustical characteristics of vibrating systems with respect to the variation of the design parameters predicting these characteristics is a necessary and important step of the acoustic design and optimization process. Acoustic design sensitivity analysis includes the computation and evaluation of the sensitivity information required for this procedure. In this study, a boundary element code performing the sensitivity analysis of the acoustic pressure by using the matrix sensitivities with respect to different design variables has been developed. The effect of the precision of boundary element discretization on the acoustic pressure sensitivity is examined via this code. The formulation is applied to a multi-source system and the dimension sensitivity analysis of near field pressures of two-dilating-spherical source is performed. The last application is devoted to a real sound source: a washing machine sitting on the floor. Sensitivity of the field pressures to the machine’s dimensions (size), surface velocity and frequency is examined on the bases of the boundary element model of the machine and half-space condition. The impacts of these variables are compared; and a limiting speed for the machine responding both the acoustical and operational requirements is determined.     

进一步改进边界元方法以克服振动声辐射计算中解的非唯一性

章利用基于三次B样条插值的边界元方法，对振动体外部声辐射问题进行了研究，对CHIEF法及其改进方法作了进一步的改进，提出在加权余量意义下，通过把内部Helmholtz积分方程与其对内点坐标取导后的方程式作线性叠加，在域外构作的一个小体积块上进行积分以形成补充方程，经与表面Helmholtz积分方程相结合，来求解任意频率下的声辐射问题，并以脉动球和摆动球作为算例，说明本提出的方法能够有效地克服在特殊频率处解的非唯一性问题。     

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...     

一维非线性声波传播特性

针对一维非线性声波的传播问题进行了有限元仿真和实验研究. 首先推导了一维非线性声波方程的有限元形式, 含有高阶矩阵的非线性项导致声波具有波形畸变、谐波滋生、基频信号能量向高次谐波传递等非线性特性. 编制有限元程序对一维非线性声波进行了计算并对仿真得到的畸变非线性声波信号进行处理, 分析其传播性质和物理意义. 为验证有限元计算结果, 开展了水中的非线性声波传播的实验研究, 得到了不同输入信号幅度激励下和不同传播距离的畸变非线性声波信号. 然后对基波和二次谐波的传播性质进行详细讨论, 分析了二次谐波幅度与传播距离和输入信号幅度的变化关系及其意义, 拟合出二次谐波幅度随传播距离变化的方程并阐述了拟合方程的物理意义. 结果表明, 数值仿真信号及其频谱均与实验结果有较好的一致性, 证实计算方法和结果的正确性, 并提出了具有一定物理意义的二次谐波随传播距离变化的简单数学关系. 最后还对固体中的非线性声波传播性质进行了初步探讨. 本研究工作可为流体介质中的非线性声传播问题提供理论和实验依据.     

换能器前辐射头与轴向相平行方向的弯曲振动

复合棒型换能器前面的变截面组件在工作时常伴有弯曲振动现象，这在一定程度上会影响换能器的工作性能；利用复合棒型换能器的纵向振动基频与前辐射头弯曲振动的恰当耦合，可展宽换能器的频带。本文用有限元法，研究了前辐射头在声换能器组成中的弯曲振动问题，与测试结果相吻合。     

Numerical modelling of ultrasonic waves in a bubbly Newtonian liquid using a high-order acoustic cavitation model

To address difficulties in treating large volumes of liquid metal with ultrasound, a fundamental study of acoustic cavitation in liquid aluminium, expressed in an experimentally validated numerical model, is presented in this paper. To improve the understanding of the cavitation process, a non-linear acoustic model is validated against reference water pressure measurements from acoustic waves produced by an immersed horn. A high-order method is used to discretize the wave equation in both space and time. These discretized equations are coupled to the Rayleigh-Plesset equation using two different time scales to couple the bubble and flow scales, resulting in a stable, fast, and reasonably accurate method for the prediction of acoustic pressures in cavitating liquids. This method is then applied to the context of treatment of liquid aluminium, where it predicts that the most intense cavitation activity is localised below the vibrating horn and estimates the acoustic decay below the sonotrode with reasonable qualitative agreement with experimental data.     

新的对角形式快速多极边界元法求解声学Helmholtz方程

传统外部声学Helmholtz边界积分方程无法在个人计算机上求解大规模工程问题. 为了有效解决这个问题, 将快速多极方法引入到边界积分方程中, 加速系统矩阵方程组的迭代求解. 由于在边界积分方程中引入基本解的对角形式多极扩展, 新的快速多极边界元法的计算效率与传统边界元相比显著提高, 计算量和存储量减少到O(N)量级(N为问题的自由度数). 包括含有420000个自由度的大型潜艇模型数值算例验证了快速多极边界元法的准确性和高效性, 清楚表明新算法在求解大规模声学问题中的优势, 具有良好的工程应用前景.     

新的对角形式快速多极边界元法求解声学Helmholtz方程

传统外部声学Helmholtz边界积分方程无法在个人计算机上求解大规模工程问题. 为了有效解决这个问题, 将快速多极方法引入到边界积分方程中, 加速系统矩阵方程组的迭代求解. 由于在边界积分方程中引入基本解的对角形式多极扩展, 新的快速多极边界元法的计算效率与传统边界元相比显著提高, 计算量和存储量减少到O(N)量级(N为问题的自由度数). 包括含有420000个自由度的大型潜艇模型数值算例验证了快速多极边界元法的准确性和高效性, 清楚表明新算法在求解大规模声学问题中的优势,     

平面叶栅气动噪声的高精度谱元方法求解

本文建立了一种用于气动噪声预测的高精度三角谱元方法。结合CBS法(Characteristic-based split method)求解Navier-Stokes方程获取伪声压声源后,基于波动方程求解声传播问题。谱元法的谱收敛特性满足了气动声学问题的高精度需求,而CBS法的引入保证了高雷诺数问题的计算稳定性。通过两组基准解问题求解验证了本文方法的正确性。将本文方法应用于平面叶栅气动噪声计算,并考察了不同攻角下噪声的变化规律。研究内容为进一步探究各类流体机械的气动噪声提供了一种新的途径。     

Numerical simulation of the ultrasonic waves generated by ring-shaped laser illumination patterns

The generation of ultrasound in aluminum plate subjected to ring-shaped laser beam illumination has been studied quantitatively by using the finite element method. The superposition effects of surface acoustic waves on the top surface and the bulk ultrasonic waves on the rear surface of specimen have been obtained in a single simulation. The typical displacement profiles of the bulk ultrasonic wave at various depths along the central axis of the ring are obtained for three different radii, and the effect of the ring radius on the focal depths of the compression and shear mode are determined. The numerical results confirm that the focal depth of a bulk acoustic mode is determined by the directivity patterns of the acoustic mode generated by point-like laser sources via a thermoelastic mechanism, which depends on the physical constants of elastic medium.     

Computation of acoustic radiation from vibrating structures in motion

The noises from a vibrating structure in motion are often encountered in engineering practice, for example, tire noise and pass-by noise of moving vehicles. Consequently, research on the radiation characteristics of moving acoustic source is of significance. In this paper, a new computational method based on the wave superposition approach is developed for the acoustic field from a vibrating structure in motion. It inherits the advantages of the wave superposition approach in the acoustic computation, and in which a method of moving simple sources is used to eliminate the influence of the Doppler effect. By the proposed method, the acoustic radiation from the moving vibrating structure can be calculated easily with the same implementation process as the conventional wave superposition approach performed in the stationary acoustic field. Finally, the validity and feasibility of the proposed method are verified by the numerical results.     

混凝土箱梁相似模型结构噪声对比分析*

为探讨混凝土箱梁噪声的时变特性,以京沪高铁32 m混凝土简支箱梁为原型,制作了1:10的缩尺模型,通过模态试验的方法验证箱梁模型与原型的相似关系,通过声学试验验证箱梁声学计算模型的正确性。然后,建立了箱梁缩尺模型与原型两种计算模型,利用有限元和边界元法求出两种模型的瞬态结构噪声。研究发现,箱梁缩尺模型与箱梁原型的材料参数满足一定关系,模型试验的方法能够验证箱梁模型与箱梁原型之间符合相似关系,箱梁模型的振动噪声测试结果能真实反映原型振动噪声水平。两种模型的结构噪声在时域内声压级及对应场点的声压存在一定相似关系。该研究可为箱梁缩尺模型结构噪声反演至箱梁原型提供依据,所采用的方法和得到的结果对桥梁结构振动与声辐射实验研究具有参考作用。     

开口/封闭薄壳体声辐射和散射的统一边界积分方程解法

推导了在二维和三维空间下开口和封闭薄壳体在任意阻抗边界条件下声辐射和散射的统一边界积分方程.相对于以前的求解方法,该方程求解声辐射和散射问题具有相同的影响矩阵,能够同时求解薄壳体气动和振动噪声的辐射和散射现象,以及分析壳体声阻抗对声波传播的影响.推导的方程可以应用于叶轮机械、管道等噪声和消声器消声性能的预测等方面.在此方程基础上,可以进一步考虑运动边界和运动介质对声辐射和散射的影响. 关键词： 薄壳体 声阻抗 积分方程 边界元方法