基于拓扑优化的声学结构材料分布设计  

DESIGN OF MATERIAL DISTRIBUTION OF ACOUSTIC STRUCTURE USING TOPOLOGY OPTIMIZATION

作　　者：杜建镔[1] 宋先凯 董立立[2] 

机构地区：[1]清华大学航天航空学院,北京100084 [2]清华大学精密仪器与机械学系,北京100084

出　　处：《力学学报》2011年第2期306-315,共10页Chinese Journal of Theoretical and Applied Mechanics

基　　金：国家自然科学基金资助项目(10672087;90816025)~~

摘　　要：针对结构的声学设计问题进行研究,通过优化两种不同的材料在结构设计域内的拓扑分布来最小化谐振结构所产生的声场中指定参考面/参考域内的声压.在研究中假定结构为线弹性小变形结构,材料阻尼为Rayleigh阻尼,声学介质为无黏、可压缩、小扰动流体.对结构响应采用有限元格式进行计算,对声场采用基于Helmholtz积分的边界元格式进行计算,由于声场在无穷远自由边界的无反射条件在边界积分中能自动得到满足,该格式特别适合于具有开放边界的声场计算.建立了结构有限元-声场边界元格式的耦合系统拓扑优化模型,导出了耦合系统敏感度分析的一般格式及伴随格式.数值算例验证了所提出的结构-声学耦合系统优化方法的有效性和可靠性,并揭示了基于声学准则的拓扑优化结果的有关特性.Analysis and design of the acoustic structure are studied in the present paper.The sound pressure on a prescribed reference plane/domain in the acoustic field that is generated by the vibrating structure is minimized by two-phase damping material distribution optimization over the structural domain.The Finite element method-Boundary element method（FEM-BEM） based structural-acoustic coupling topology optimization model is established.The sensitivities of the coupling variables with respect to the design variables are derived by using the direct differentiation method as well as the adjoint method.It is pointed out that the adjoint method provides the more efficient formulation for sensitivity analysis when the amount of the reference field points on the reference surface for sound pressure calculation is much less than the total amount of the design variables.The proposed methods are validated by numerical examples of the designs of the traveling wave tube and the motor cover.Some interesting features on optimum topologies obtained from the structural-acoustic coupling designs are revealed and discussed.

关 键 词：边界积分 结构声学耦合系统 拓扑优化 敏感度分析 伴随方法 

分 类 号：TB535[理学—物理]