求解二维结构-声耦合问题的一种直接方法

DIRECT SOLUTION TO 2-D SOUND-STRUCTURE INTERACTION PROBLEMS

本文基于传递矩阵法 (TMM)和虚拟边界元法 (VBEM ) ,提出了一种求解在谐激励作用下二维结构 -声耦合问题的直接法。文中对任意形状的二维弹性环建立了一阶非齐次运动微分方程组 ,便于用齐次扩容精细积分法求解 ,对于含有任意形状孔穴的无穷域流体介质的Helmholtz外问题 ,采用复数形式的Burton_Miller型组合层势法建立了虚拟边界元方程 ,保证了声压在全波数域内存在唯一解。根据叠加原理并结合最小二乘法 ,提出了一种耦合方程的直接解法 ,由于该方法不存在迭代过程 ,因而具有较高的计算精度和效率。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 。

Based on transfer matrix method(TMM)and virtual boundary element method(VBEM),proposed a direct solution to 2-D sound-structure interaction problem under harmonic excitation is proposed.The first-order non-homogeneous motion equations that are formulated for an elastic ring with arbitrary geometrical shape can be easily solved by the homogenized direct integration with high precision.The Burton-Miller's complex number combined-lay potential method is adopted for establishing the VBEM equations of exterior Helmholtz problem with complex geometrical cavity in infinite fluid domain,thus,the uniqueness of acoustic pressure can be ensured for all wave-numbers.By virtue of superposition principle combined with the least square approximation,a direct solution to the coupled equations is presented.Owing to noniterative procedure,higher accuracy and efficiency can be achieved by using the method proposed in the paper,The examples of acoustic radiation from two typical fluid-loaded elastic rings under a harmonic concentrated force are presented.Numerical results show that the proposed method is more effcient than the mixed FE-BE method in common use.