WB法分析声腔的中频响应

Wave Based Method for Mid-Frequency Vibration Analysis of a Cavity

分析振动-声的数值方法主要是基于单元的方法,如有限元和边界元。由于计算效率低,基于单元的方法在实际中约束在低频段。近年来,基于间接Trefftz法的WB(W ave Based)法得到了发展。与基于单元的方法相比,结构和声域都不再需要划分成更小的单元以及在每个单元内采用简单、近似的形函数来求解动力学方程,而是整个域内的压力场由精确满足动力学方程齐次部分的波函数和满足动力学非齐次方程的特解函数组成。波函数的常数系数通过加权余量或者最小二乘法得到。基于二维的例子讨论了这种方法的收敛特性并与有限元结果进行了比较。结果表明WB法比有限元法计算效率更高以及更好的收敛特性。

The main numerical modelling techniques for vibro -acoustic analysis are based on element based method, such as the finite element and boundary element method. Due to the huge computational efforts, the use of these methods is practically restricted to low frequency applications. Recently, a new wave based prediction technique has been developed which is based on the indirect Trefftz approach In contrast with the finite element method, in which the acoustic domains are discretized into small elements and the steady -state dynamic equations are solved within each element using simple, approximate shape functions, the pressure field within the entire of the acoustic domains are approximated in terms of wave functions, which are exact solutions of the homogeneous parts of the dynamic equations and the particular solutions , which are exact solutions of the inhomogeneous dynamic equations. The contributions of the wave functions to the vibro - acoustic response are determined by applying the boundary conditions in a weighted residual formulation or Least - squares formulation. This paper discusses the convergence properties of the newly developed method, based on its application for a two -dimensional example and compare with the FEM＇s results. The results show that the proposed method is more efficient than the FEM and better convergence properties.