A topology optimization method for coupled vibro-acoustic problem based on hybrid finite element-wave based method is proposed. The hybrid finite element-wave based method is used to model the coupled free layer damping structure-acoustics system, and a gradient-based topology optimization formulation is developed by solid isotropic microstructures with penalization method, to obtain optimized layout of free layer damping with the objective of minimizing sound pressure in the acoustic cavity and with constraint defined as the amount of free layer damping. The adjoint variable method for the coupled vibro-acoustic model based on the hybrid finite element-wave based method is also derived as a part of the sensitivity analysis. Numerical example shows that the optimized distribution reduce sound pressure effectively and the calculation time of proposed method is less than the conventional method for topology optimization base on finite element method. Experimental results verify the accuracy of the hybrid finite element-wave based method and the effect of optimized damping material layout is also validated by experiment.

提出了一种基于混合有限元波方法的声振耦合问题拓扑优化方法。采用基于混合有限元波的方法对耦合的自由层阻尼结构-声学系统进行建模，并通过固体各向同性微结构和惩罚方法开发基于梯度的拓扑优化公式，以获得优化的自由层阻尼布局。目标是最小化声腔中的声压，并将约束定义为自由层阻尼量。基于混合有限元波方法的耦合振动声学模型的伴随变量方法也作为灵敏度分析的一部分推导出来。数值算例表明，优化后的分布有效地降低了声压，并且该方法的计算时间少于基于有限元法的常规拓扑优化方法。实验结果验证了基于混合有限元波的方法的准确性，并通过实验验证了优化阻尼材料布局的效果。