开口结构声辐射计算的虚拟边界法

计算薄壁开口结构声辐射问题时,一般采用以结构表面压力差作为变量的间接边界元法.当结构两表面的法向量不一致或者两表而振动速度不相等时,间接边界元法无法应用,只能采用直接边界元对结构的内外边界均进行离散求解.对于厚度较小的结构,内外表面均离散的直接边界元法会导致数值积分奇异的困难.针对上述不足,文章提出一种计算开口结构声辐射问题的虚拟边界法:在开口结构上人为地加上边界,使其成为一个或多个相互独立的封闭结构,对这样的封闭结构分内外声场分别建立方程,并利用虚拟边界上的压力和速度连续条件联立求解,从而避免了间接边界元和直接边界元法计算开口结构声辐射问题时存在的缺陷;同时采用文中的方法还可以同时得到声场中非物面边界上质点的振动速度和压力,这是常规边界元法无法做到的.数值算例表明文中的方法是正确可行的.

Virtual Boundary Method for Solving Acoustic Problems of Open Structure

Indirect boundary element method (IDBEM) is often applied in solving acoustic problems for open structure.This method is based on the condition that the normal vectors and the amplitude of vibration velocity on each face of the open structure are to be the same.If all these condition are not satisfied, IDBEM can not be used. Thus direct boundary element method (DBEM) has to be applied for the analysis of open structure,which needs to mesh both the surfaces of the structure. However, singular or near singular integral will appear in DBEM when the structure is very thin. In order to overcome the difficulties in solving acoustic problems of open structure for both IDBEM and DBEM,a new formula called virtual boundary method is presented.In this method,some virtual boundaries are added to the structure,thus make the open structure be closed and separate the acoustic region into two independent regions,i.e.interior and exterior regions.The acoustic boundary integral equations for each region can be formulated independently. The two equations are then coupled and solved according to the pressure and velocity continuum condition on the virtual boundaries.Moreover, the sound pressure and velocity on the virtual boundaries can be get simultaneity by using this method, which cannot be done by conventional boundary element method. Numerical results show that this method is correct and feasible.