求解二维结构-声耦合问题的一种半数值半解析方法

A SEMI-ANALYTICAL AND SEMI-NUMERICAL METHOD FOR SOLVING 2-D SOUND-STRUCTURE INTERACTION PROBLEMS

基于传递矩阵法和虚拟源强模拟技术提出了一种求解在谐激励作用下二维结构 声相互作用问题的半数值半解析法 .在足够小的积分步长内 ,文中对任意形状弹性环沿周向曲线坐标的非齐次状态微分方程组 ,建立了一种齐次扩容方法 .对于外声场 ,采用多圆形虚拟源强配置方案 ,并在每一条圆形配置曲线上将源强密度函数用Fourier级数展开 ,同时结合快速Fourier变换法 ,提出了一种高精度、高效率求解任意形状二维孔穴Helmholtz外问题的快速算法 .在耦合方程的求解方面 ,根据叠加原理 ,将外激励和虚拟源强的Fourier级数展开项作为广义力分别作用在弹性环上 ,借助齐次扩容方法和精细积分法求得弹性环的状态向量 ,再利用流固交接条件和最小二乘法直接建立了耦合系统的求解方程 .文中给出了二个典型弹性环在集中谐激励力作用下声辐射算例 ,计算结果表明该文方法较通常采用的混合FE BE法更为有效 .

Based on the transfer matrix method and the virtual source simulation technique, this paper proposes a novel semi-analytical and semi-numerical method for solving 2-D sound- structure interaction problems under a harmonic excitation.Within any integration segment, as long as its length is small enough,along the circumferential curvilinear coordinate,the non- homogeneous matrix differential equation of an elastic ring of complex geometrical shape can be rewritten in terms of the homogeneous one by the method of extended homogeneous capacity proposed in this paper.For the exterior fluid domain,the multi-circular virtual source simulation technique is adopted.The source density distributed on each virtual circular curve may be ex- panded as the Fourier's series.Combining with the inverse fast Fourier transformation,a higher accuracy and efficiency method for solving 2-D exterior Helmholtz's problems is presented in this paper.In the aspect of solution to the coupling equations,the state vectors of elastic ring induced by the given harmonic excitation and generalized forces of coefficients of the Fourier series can be obtained respectively by using a high precision integration scheme combined with the method of extended homogeneous capacity put forward in this paper.According to the superposition princi- ple and compatibility conditions at the interface between the elastic ring and fluid,the algebraic equation of system can be directly constructed by using the least square approximation.Examples of acoustic radiation from two typical fluid-loaded elastic rings under a harmonic concentrated force are presented.Numerical results show that the method proposed is more efficient than the mixed FE-BE method in common use.