Abstract In this study, we examine an acoustic–structure interaction problem for nonproportionally damped systems. Coupled responses for a structure and acoustic enclosure are derived using a modified modal coupling formulation. Uncoupled modal patterns are used to assess the coupling effectiveness. Comparison with a proportional damping case reveals characteristics that associate complex modes with damping optimality. Such an interrelation is investigated through topology optimization of a damping layer to minimize the acoustic pressure in the cavity. The findings of this numerical study indicate a spatial relation between the imaginary part of the coupling coefficient and the optimal damping layout. Further investigation of complex modal patterns with wave interpretation shows that the optimal damping characteristics of the panel can be expressed by a spatially varying nonproportional damping index. Case studies involving various nonproportional damping configurations are presented to confirm the significant correlation with respect to observed phenomena.

中文翻译：

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阻尼分布对板腔系统耦合的影响：通过模态方法实现最优的条件

摘要 在这项研究中，我们研究了非比例阻尼系统的声学-结构相互作用问题。结构和隔音罩的耦合响应是使用修改后的模态耦合公式得出的。非耦合模态模式用于评估耦合有效性。与比例阻尼情况的比较揭示了将复杂模式与阻尼优化相关联的特征。通过对阻尼层进行拓扑优化以最小化腔中的声压来研究这种相互关系。该数值研究的结果表明耦合系数的虚部与最佳阻尼布局之间存在空间关系。通过波浪解释对复杂模态模式的进一步研究表明，面板的最佳阻尼特性可以通过空间变化的非比例阻尼指数来表示。介绍了涉及各种非比例阻尼配置的案例研究，以确认与观察到的现象的显着相关性。