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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面振动速度不相等时,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。
When calculating the sound radiation problem of the thin-walled open structure, the indirect boundary element method using the pressure difference of the structure surface as a variable is generally adopted. The indirect boundary element method can not be applied when the normal vectors of two surfaces of the structure are not consistent or the velocities of the two surfaces are not equal. Only the direct boundary element can be used to discretize the inner and outer boundaries of the structure. For structures with smaller thickness, the direct boundary element method with discrete inner and outer surfaces leads to the difficulty of numerical integration singularity. In view of the above shortcomings, the article proposes a virtual boundary method to calculate the sound radiation problem of the open structure: artificially add the boundary to the open structure so that it becomes one or more independent closed structures. For such a closed structure, the internal and external sound fields The equations are established respectively and the pressure and velocity continuous conditions on the virtual boundary are used to solve the problem simultaneously. This method avoids the shortcomings of the indirect boundary element and the direct boundary element method in calculating the acoustic radiation of the open structure. Simultaneously, The vibration velocity and pressure of the particle on the non-object boundary in the sound field can not be achieved by the conventional boundary element method. Numerical examples show that the method in this paper is correct and feasible.