Abstract This paper presents a new sensitivity analysis method for coupled acoustic–structural systems subjected to non-stationary random excitations. The integral of the response power spectrum density (PSD) of the coupled system is taken as the objective function. The thickness of each structural element is used as a design variable. A time-domain algorithm integrating the pseudo excitation method (PEM), direct differentiation method (DDM) and high precision direct (HPD) integration method is proposed for the sensitivity analysis of the objective function with respect to design variables. Firstly, the PEM is adopted to transform the sensitivity analysis under non-stationary random excitations into the sensitivity analysis under pseudo transient excitations. Then, the sensitivity analysis equation of the coupled system under pseudo transient excitations is derived based on the DDM. Moreover, the HPD integration method is used to efficiently solve the sensitivity analysis equation under pseudo transient excitations in a reduced-order modal space. Numerical examples are presented to demonstrate the validity of the proposed method.

中文翻译：

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非平稳随机激励下声结构耦合系统的随机灵敏度分析

摘要 本文提出了一种新的非平稳随机激励下声-结构耦合系统的灵敏度分析方法。以耦合系统响应功率谱密度(PSD)的积分作为目标函数。每个结构元件的厚度用作设计变量。提出了一种集成伪激励法(PEM)、直接微分法(DDM)和高精度直接(HPD)积分法的时域算法，用于目标函数相对于设计变量的敏感性分析。首先，采用PEM将非平稳随机激励下的灵敏度分析转化为伪瞬态激励下的灵敏度分析。然后，基于DDM推导出伪瞬态激励下耦合系统的灵敏度分析方程。此外，HPD积分方法用于在降阶模态空间中有效地求解伪瞬态激励下的灵敏度分析方程。给出了数值例子来证明所提出方法的有效性。