Sensitivity analysis of coupled acoustic-structural systems under non-stationary random excitations is investigated in this paper. The combined method of direct differentiation method (DDM) and pseudo excitation method (PEM) in previous work is computationally expensive for problems with large-scale design variables. To circumvent this difficulty, a fast sensitivity analysis method integrating the adjoint variable method (AVM) and PEM for coupled acoustic-structural systems under non-stationary random excitations is proposed. In this framework, the sensitivity analysis of coupled systems subject to non-stationary random excitations is transformed into a sensitivity analysis under pseudo-transient excitations with the help of PEM. On this basis, the computing efficiency of random response sensitivity is improved directly by solving the adjoint equations involved in the AVM. Numerical examples fully demonstrate the accuracy and efficiency of the proposed method.

本文研究了非平稳随机激励下耦合声-结构系统的灵敏度分析。先前工作中直接微分法 (DDM) 和伪激励法 (PEM) 的组合方法对于具有大规模设计变量的问题在计算上是昂贵的。为了克服这个困难，提出了一种结合伴随变量法（AVM）和PEM的非平稳随机激励下耦合声结构系统的快速灵敏度分析方法。在该框架中，在 PEM 的帮助下，受非平稳随机激励的耦合系统的灵敏度分析转化为伪瞬态激励下的灵敏度分析。在此基础上，通过求解AVM中涉及的伴随方程，可以直接提高随机响应灵敏度的计算效率。数值例子充分证明了所提出方法的准确性和效率。