声振耦合声场分析与声辐射结构优化

Analysis of vibro-acoustic coupling sound field and sound radiation optimization

摘要:

为实现内声场和外声场同时存在的强耦合声辐射预报和噪声优化,建立有限元/边界元强耦合方程,并给出两种声功率灵敏度的求解方法。首先给出结构和内声场的声振耦合有限元方程,并考虑外声场声介质对结构的反作用,根据交界面力和法向速度的连续性建立有限元/边界元强耦合方程；然后针对声功率拓扑优化中单元灵敏度分析时难以解耦的问题,将声功率转化为以结构位移为变量的表达形式,并修改伴随方程,实现将该方法扩展至强耦合优化问题中；同时针对伴随变量法(adjoint variable method,AVM)推导过程复杂的问题,提出声功率灵敏度的直接求导法；最后采用线性化刚度方法将结构单元相对密度作为连续设计变量,对不同的结构材料和声介质组合优化问题展开研究。对比计算表明:该耦合模型计算的响应值与采用无反射边界的有限元法计算结果基本吻合；直接求导法和伴随变量法均可使迭代达到收敛,但直接求导法推导过程更简洁高效；数值优化算例证明优化算法的适用性较好,在声功率优化设计中的有效性。

Abstract:

To realize the prediction of strongly coupled sound radiation and the optimization of noise in both internal and external sound fields, the finite element/boundary element coupling equation was established, and two methods for solving the sensitivity of sound power were proposed. First, the coupled finite element equations of the structure and the internal sound field were given. Considering the interaction of the external acoustic medium to the structure, the finite element/boundary element coupling equation was established according to the continuity of interface force and normal velocity. Then, in view of the difficulty of decoupling in element sensitivity analysis in sound power topology optimization, the sound power was converted into an expression with structural displacement as variable, and the adjoint equation was modified to realize the extension of the method to the strongly coupled optimization problem. The direct derivation method of sound power sensitivity was proposed considering the complicated derivation process of the adjoint variable method (AVM). Finally, the linearized stiffness method was adopted, which takes the relative density of structural elements as continuous design variables, and the optimization of different structural materials and acoustic media was studied. Comparison results show that the sound power calculated by the coupled model was consistent with that of the finite element method without reflection boundary. Both direct derivation method and AVM could quickly achieve convergence, but the derivation process of the direct derivation method was more concise and efficient. Numerical optimization proves that the optimization algorithm has good applicability and is effective in sound power optimization design.