关键词: 子波, Helmholtz积分方程, 有限元, 声振耦合

Abstract: A spectral method in which wavelets are used as the basis functions is developed for solving acoustic and coupled structural-acoustic problems.On the basis of axisymmetric boundary integral formulation for axisymmetric bodies with arbitrary boundary conditions,the boundary quantities are expanded in wavelet series along the generator of the body,and a wavelet spectral formulation for solving acoustic problems of axisymmetric bodies is derived.Then, coupled wavelet spectral and finite element method is formulated for solving sound-structure interaction of axisymmetric elastic bodies with arbitrary boundary conditions.In this coupled method,a three-dimensional formulation is reduced to a one-dimensional one along the generator of the body.The coupled system is solved using the superposition principle for all the terms of Fouries series.The analysis of a submerged structure is performed.The comparisons of results based on the new technique with coupled finite element and boundary element methods are presented.Numerical solutions are given which show the fast convergence and the high accuracy.

Key words: wavelet, Helmholtz integral equation, coupled wavelet spectral and finite element method, sound-structure interaction