Acoustic diffraction effects at the Hellenistic amphitheater of Epidaurus: seat rows responsible for the marvelous acoustics

The Hellenistic theater of Epidaurus, on the Peloponnese in Greece, attracts thousands of visitors every year who are all amazed by the fact that sound coming from the middle of the theater reaches the outer seats, apparently without too much loss of intensity. The theater, renowned for its extraordinary acoustics, is one of the best conserved of its kind in the world. It was used for musical and poetical contests and theatrical performances. The presented numerical study reveals that the seat rows of the theater, unexpectedly play an essential role in the acoustics--at least when the theater is not fully filled with spectators. The seats, which constitute a corrugated surface, serve as an acoustic filter that passes sound coming from the stage at the expense of surrounding acoustic noise. Whether a coincidence or not, the theater of Epidaurus was built with optimized shape and dimensions. Understanding and application of corrugated surfaces as filters rather than merely as diffuse scatterers of sound, may become imperative in the future design of modern theaters.     

Calculation of sound radiant efficiency and sound radiant modes of arbitrary shape structures by BEM and general eigenvalue decomposition

In this paper, a numerical method is presented to calculate sound radiant efficiency and radiant modes of arbitrary shape structures. Some methods have been proposed to compute sound radiant efficiencies and sound radiant modes of plates and beams. However, there is not a valid method to calculate for arbitrary shape structures except for measurement at the present time. The method proposed can predicate the sound radiant efficiencies and the sound radiant modes for arbitrary shape structures by boundary element method (BEM) and general eigenvalue decomposition. The validity of this method is demonstrated by two numerical examples of pulsating sphere and radiation cube.     

An investigation of the sound field above the audience in large lecture halls with a scale model

Measurements of steady-state sound pressure levels above the audience in large lecture halls show that the classical equation for predicting the sound pressure level is not accurate. The direct field above the seats was measured on a 1:10 scale model and was found to be dependent on the incidence angle and direction of sound propagation across the audience. The reverberant field above the seats in the model was calculated by subtracting the direct field from the measured total field and was found to be dependent on the magnitude and particularly on the placement of absorption. The decrease of sound pressure level versus distance in the total field depends on the angle (controlled by absorption placement) at which the strong reflections are incident upon the audience area. Sound pressure level decreases at a fairly constant rate with distance from the sound source in both the direct and reverberant field, and the decrease rate depends strongly on the absorption placement. The lowest rate of decay occurs when the side walls are absorptive, and both the ceiling and rear wall are reflective. These consequences are discussed with respect to prediction of speech intelligibility.     

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.     

一种水平变化波导中声传播问题的耦合模态法

针对介质参数及海底边界水平变化波导中的声传播问题,本文基于多模态导纳法提出一种能量守恒且便于数值稳定求解的耦合模态方法.将声压表示为一组正交完备的本地本征函数之和,对声压满足的Helmholtz方程在本地本征函数上作投影,推导出关于声压模态系数的二阶耦合模态方程组.耦合矩阵直观描述水平变化因素对模态耦合的贡献.为避免直接求解二阶耦合模态方程组可能遇到的数值发散问题,将其重构为两个耦合的一阶演化方程组,引入导纳矩阵并使用Magnus数值积分方法获得稳定的声场解.利用该耦合模态方法数值计算水平变化波导中的声场,并与COMSOL参考解比较,结果表明该耦合模态理论能够精确求解水平变化波导中的点源及分布源传播问题.     

Boundary element-free method for elastodynamics

The moving least-square approximation is discussed first. Sometimes the method can form an ill-conditioned equation system, and thus the solution cannot be obtained correctly. A Hilbert space is presented on which an orthogonal function system mixed a weight function is defined. Next the improved moving least-square approximation is discussed in detail. The improved method has higher computational efficiency and precision than the old method, and cannot form an ill-conditioned equation system. A boundary element-free method (BEFM) for elastodynamics problems is presented by combining the boundary integral equation method for elastodynamics and the improved moving least-square approximation. The boundary element-free method is a meshless method of boundary integral equation and is a direct numerical method compared with others, in which the basic unknowns are the real solutions of the nodal variables and the boundary conditions can be applied easily. The boundary element-free method has a higher computational efficiency and precision. In addition, the numerical procedure of the boundary element-free method for elastodynamics problems is presented in this paper. Finally, some numerical examples are given.     

Boundary element-free method for elastodynamics

1 Introduction In recent years, more and more attention has been paid to researches on the meshless (or meshfree) method, which makes it a hot direction of computational mechanics[1,2]. The meshless method is the approximation based on nodes, then the large deformation and crack growth problems can be simulated with the method without the re-meshing technique. And the meshless method has some advantages over the traditional computa- tional methods, such as finite element method (FEM) and boun…     

部分浸没圆柱壳声固耦合计算的半解析法研究

部分浸没圆柱壳-流场耦合系统的声振分析是一种典型的半空间域内声固耦合问题,其振动及声学计算目前主要依赖于数值方法求解,但无论从检验数值法还是从机理上揭示其声固耦合特性,解析或半解析方法的发展都是不可或缺的.本文提出了一种半解析方法,先将声场坐标系建立在自由液面上,采用正弦三角级数来满足自由液面上的声压释放边界条件;接着基于二维Flügge薄壳理论建立了以圆柱圆心为坐标原点的壳-液耦合系统的控制方程;然后再利用Galerkin法处理声固耦合界面的速度连续条件,推导得到声压幅值与壳体位移幅值之间的关系矩阵并求解该耦合系统的振动和水下声辐射.与有限元软件Comsol进行了耦合系统自由、受迫振动和水下辐射噪声计算结的对比分析,表明本文方法准确可靠.本文的研究为解析求解弹性结构与声场部分耦合的声振问题提供了新的思路.     

An energy-conserving two-way coupled mode model for underwater acoustic propagation

In order to avoid the energy non-conservation in two-way sound field calculations,which results from certain approximation of non-horizontal boundary,an energy-conserving twoway coupled mode propagation model is developed.During the derivation of this model,the non-horizontal boundary condition is treated strictly instead of making an approximation.The coupling equations,which are easy to numerical implementation,are derived from the equation of motion and the equation of continuity.Moreover,the validity of this model is illustrated with several numerical examples of different bottom parameters and the equation of energy conservation.It is shown that a boundary correction is introduced by the strict formulizing of the boundary condition in this model.This boundary correction guarantees the coupling coefficients being symmetrical and makes the sound fields satisfy the energy conservation.Thus,the energy-conserving coupled model is able to handle non-horizontal boundaries adequately,and the two-way sound fields in a non-horizontal stratified media can be calculated exactly by this model.     

A meshless Galerkin method with moving least square approximations for infinite elastic solids

Combining moving least square approximations and boundary integral equations, a meshless Galerkin method, which is the Galerkin boundary node method （GBNM）, for twoand three-dimensional infinite elastic solid mechanics problems with traction boundary conditions is discussed. In this numerical method, the resulting formulation inherits the symmetry and positive definiteness of variational problems, and boundary conditions can be applied directly and easily. A rigorous error analysis and convergence study for both displacement and stress is presented in Sobolev spaces. The capability of this method is illustrated and assessed by some numerical examples.