求解水下非圆弹性环声散射问题的一种半解析方法

基于传递矩阵法、齐次扩容精细积分法和复数矢径虚拟边界谱方法 ,提出了一种求解水下非圆弹性环声散射问题的半解析方法。该方法具有以下几个优点 :(1)采用复数矢径虚拟边界谱方法 ,不仅能保证在全波数域内Helmholtz外问题解的唯一性 ,而且由于虚拟源强密度函数采用 Fourier级数展开 ,克服了用单元离散解法不能用于较高频率范围的缺点 ;(2 )采用齐次扩容精细积分法求解非圆弹性环的状态微分方程 ,其计算结果具有很高的精度 ;(3)耦合方程不需要交错迭代求解 ,提高了计算效率。文中给出了两个典型非圆弹性环在平面声波激励下的声散射算例 ,计算结果表明本文方法是一种求解二维非圆弹性环声散射问题非常有效的半解析法。

A novel semi-analytical method of solving acoustic scattering problems for non-circular elastic rings

Based on the transfer matrix method, the homogenizatied direct integration metho d with high precision and the spectrum method of virtual boundary with comp lex radius vector, a novel semi-analytical method of solving acoustic scatteri n g problems for non-circular elastic rings is proposed. The advantages of this m ethod are as follows: (1)Adopting the spectrum method of virtual boundary with c o mplex radius vector, not only the uniqueness of solution of exterior Helmholtz p roblem for all wave-numbers is ensured, but the shortcoming of the disc r etized element methods such as FEM and BEM et al, not to be available in higher -frequenc y range can be overcame effectually due to expanding the source density distribu ted on virtual integral boundary as Fourer's series; (2) introducing the homogen i zatied direct integration method with high precision to solve the first-order n on-hom ogeneous motion equations of an elastic ring with arbitrary geometrical shape, i ts computational results can be obtained with very high accuracy; (3) Owing to n o iterative procedure for the coupled equations, the efficiency of computation can be greatly improved. The examples of acoustic scattering from two typical non- c ircular elastic rings under exciting by a planar sound wave are presented. Numer ical results show that the proposed method is a very efficient semi-analytical m ethod of solving acoustic scattering problems for 2D non-circular elastic rin gs.