基于有限元与宽频快速多极边界元的二维流固耦合声场分析

采用有限元/快速多极边界元法进行水下弹性结构的辐射和散射声场分析。Burton-Miller法用于解决传统单Helmholtz边界积分方程在求解外边界值问题时出现的非唯一解的问题。该文采用GMRES和快速多极算法加速求解系统方程。针对传统快速算法在高频处效率低和对角式快速算法在低频处不稳定这一问题,该文通过结合这两种快速算法形成宽频快速算法来克服。同时该文通过观察不同参数条件设置下,宽频快速多极法得到的数值结果在计算精度和计算时间上的变化,得到最优的参数组合值。最后通过数值算例验证该文算法的正确性和有效性。     

简支梁在无限大不可压缩流体和声学流体中的固有振动问题

本文用边界积分方程描述无限大声学流体,从而得到了控制圆截面简支梁在该流体中固有振动的积分-微分方程。在此方程基础上,分别用摄动法和有限元与摄动展开相结合的方法,计算了简支梁在无限大声学流体中的固有频率。当声速趋于无穷大时,得到了无限大不可压缩流体中简支梁的固有频率。本文的方法可推广到较为复杂的结构声辐射系统的固有频率的计算上。     

A new boundary element method for resonance of an acoustic enclosure

Abstract

This paper presents a new boundary element formulation in which the eigenvalue appears outside the integral operator, which distinguishes it from the Helmholtz integral equation. Thus, the formation of global matrices need only be assembled once. Since the kernel of the operator used in the new formulation is real‐valued, all calculations can be carried out in a much simpler way in the real domain. The complex acoustic pressure amplitude is considered herein to deivate by a certain amount from a harmonic function. It is an important contribution that an exact relation between the deviator and the complex acoustic pressure amplitude is constructed locally and thus no more approximations are introduced except conventional boundary discretizations. Several examples are given to illustrate the feasibility of an accurate, effective prediction of resonance.     

声学-结构设计灵敏度分析

声学 -结构设计灵敏度分析揭示了结构振动引起的辐射声压与结构设计变量之间的关系。分别用有限元法和边界元法计算结构设计灵敏度和声学灵敏度。将两个灵敏度结合得到最终的声学 -结构设计灵敏度。在边界元计算中 ,采用退化元处理奇异积分问题 ,对特征频率不唯一问题采用CHIEF方法处理。以脉动球和箱体为例 ,验证了算法的可行性和精确性。     

论Helmholtz方程的一类边界积分方程的合理性

本文导出了Helmholtz 方程超定边值问题有解的一个充要条件,和用非解析开拓法证明了文[1]中的Helmholtz 方程在外域中的解的边界积分表示式的合理性,并将此类边界积分表示式推广用于带空洞的有限域。这样就比较严密而又浅近地证明了基于该表示式建立起来的间接变量和直接变量边界积分方程的合理性。     

车用制动空气压缩机结构辐射噪声特性研究

针对某公司生产的KYV480型号车用制动活塞式空气压缩机(简称:空压机)运行过程中,振动噪声较大,一定程度上影响了驾驶员和乘客的乘车舒适性和身心健康的情况,文章基于有限元和声学边界元联合求解的方法对空压机的结构表面辐射噪声特性进行研究.在计算得到空压机运行过程中壳体所受载荷的基础上,对空压机壳体表面的振动加速度响应进行...     

降阶单元的新进展：内置了最大模误差估计器的自适应有限元法初探

该文基于初值问题中降阶单元的成功实践,进一步对一般边值问题提出无需超收敛计算、无需结构化网格、无需结点位移修正的降阶单元;进而提出以降阶单元作为最终解,且内置了最大模误差估计器的自适应有限元算法。该文对这一研究进展做简要介绍,并给出一维和二维边值问题的初步算例,以展示本法的可行性、有效性和可靠性。     

汽车内部声场分析

在新车身设计阶段,由于汽车内部诸多因素的不确定,用有限元计算声腔模态时对声腔模型进行了简化处理。对比了有无座椅和仪表盘挡板的车内声学模态结果,用边界元法进行了车内结构辐射声压计算和声贡献量分析,对改进车内噪声有一定参考。     

EXPLOITING DESIGN LENGTH SCALES IN STRUCTURAL OPTIMIZATION

Many structural optimization methods use geometric length scales as well as artificially imposed lengths such as finite element dimensions. One considers functions defined over these dimensions in characterizing and solving the problem. The natural length scales involved in the proposed design change are generally overlooked. When one proposes an optimization based on change of certain panels in a sheet metal structure, for instance, it might be helpful to use the dimensions of the redesign areas as characteristic lengths. In the present study, a Rayleigh–Ritz approach is taken where the responses of a structure to pseudo-loads (acting only over specified design-change regions) are employed as basis vectors. It is found that convergence of the optimization process is improved. The method is demonstrated for moderate-sized problems, and as with other modal methods, should become even more helpful for large problems. The new complexity involved is the requirement for a type of problem-dependent linking, in parallel with the conventional design variable linking. This can be automated. © 1997 by John Wiley & Sons, Ltd.     

体积源边界点法及其在声辐射计算中的应用

利用作者提出的体积源边界点法，对结构振动声辐射的计算问题进行了研究。给出了该法在全频率范围内存在唯一解的数学证明；通过诸多不同边界曲面和不同边界量分布的声辐射算例，从计算精度、计算稳定性、对振动体任意表面几何形状的适应性以及克服解的非唯一性等方面，对该方法的有效性进行了检验。     

Towards error bounds of the failure probability of elastic structures using reduced basis models

Structural reliability methods aim at computing the probability of failure of systems with respect to prescribed limit state functions. A common practice to evaluate these limit state functions is using Monte Carlo simulations. The main drawback of this approach is the computational cost, because it requires computing a large number of deterministic finite element solutions. Surrogate models, which are built from a limited number of runs of the original model, have been developed, as substitute of the original model, to reduce the computational cost. However, these surrogate models, while decreasing drastically the computational cost, may fail in computing an accurate failure probability. In this paper, we focus on the control of the error introduced by a reduced basis surrogate model on the computation of the failure probability obtained by a Monte Carlo simulation. We propose a technique to determine bounds of this failure probability, as well as a strategy of enrichment of the reduced basis, based on limiting the bounds of the error of the failure probability for a multi‐material elastic structure. Copyright © 2017 John Wiley & Sons, Ltd.     

SOLVING NONLINEAR DIFFERENTIAL EQUATIONS OF MECHANICS WITH THE BOUNDARY ELEMENT METHOD AND RADIAL BASIS FUNCTIONS

The Boundary Element Method is a very effective method for solving linear differential equations. To use it also in the consideration of non-linear problems some different procedures were developed, among them the dual reciprocity method and the particular integral method. Both procedures use interpolation conditions for the approximation with radial basis functions. In this paper a method is presented which avoids problems connected with interpolation by means of quasi-interpolation. It is possible to solve differential equations of the kind Δ^mu=p(u) approximately; the application to two non-linear problems of plate theory yield good results. Hints to a theoretical examination of the method including sufficient conditions for feasibility and convergence are given. © 1997 by John Wiley & Sons, Ltd.     

Boundary element analysis of wave-current interaction around a large structure

A numerical approach for wave-current interaction around a large structure is investigated, based on potential flow theory, linear waves and small current velocity approximation. The velocity potential in a wave-current coexisting field is separated into a steady current potential and an unsteady wave potential. The boundary element method was then employed to compute the unsteady wave potential with effects of both a uniform current and a large body taken into consideration. It is demonstrated that the steady current potential can be expressed as the sum of a uniform current and a steady disturbance due to the presence of the object. The variation of current velocity in the vicinity of the object is then calculated by using a surface vorticity boundary integral meethod. Boundary element analysis is also used for the numerical solutions of the surface vorticity method. Substituting both unsteady wave potential and current velocity into the first-order dynamic surface boundary condition, the water surface elevation around a large structure in a wave-current coexisting field can then be obtained. Comparisons of numerical predictions with experimental results ar also made; qualitative good agreements are obtained.     

基于等效参数反演的结构覆盖层声学性能预报

文章基于等效参数反演的方法研究了结构覆盖层对弹性平板的声散射特性影响。根据结构覆盖层声特性的实验测量结果,基于遗传算法进行反演得到具有相同声学性能的结构覆盖层声学参数;再利用有限元耦合边界元方法分别计算了弹性平板和有限长圆柱壳敷设覆盖层前后的散射声场,获得敷设覆盖层前后的声目标强度;最后,通过消声水池试验测量单、双层平板敷设覆盖层前后的散射声场,与理论仿真结果进行对比。采用覆盖层等效参数计算得到的单、双层平板敷设覆盖层前后的散射声场中目标回波强度差值与试验测量结果的误差在3 dB以内。结果表明根据遗传算法建立的结构覆盖层等效参数反演模型可以用于预报复杂结构覆盖层的声学特性。