This paper presents a stability-preserving model reduction approach for a vibro-acoustic finite element model including poroelastic materials. Most of the research on these systems in the past was conducted in the frequency domain and there were less focus on the stability properties. However, with the increasing of interest in time-domain auralization and virtual sensing, stability-preserving model order reduction is becoming essential for efficient time-domain simulations. The original finite element models for such systems are already well established but not extended to the time domain because of its high computational demand. Therefore, this paper proposes a method to generate stable reduced-order models. The solid displacement–total displacement () formulation of the Biot’s model is used to describe the poroelastic media. This formulation leads to a set of positive and symmetric system matrices with passive transfer functions. Applying the Kalman–Yakubovich–Popov lemma and the Cholesky/LDL decomposition, this formulation is modified to satisfy the previously proven stability-preserving conditions under one-sided model order reduction. Furthermore, the coupling conditions between the poroelastic media, air, and structure are also investigated. It is finally shown that the stability-preserving property is kept for the coupled models with appropriate variables. The proposed method is verified by several numerical simulations.

中文翻译：

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多孔弹性材料时域振动声学有限元模拟的模型降阶


本文提出了一种用于包含多孔弹性材料的振动声学有限元模型的保稳模型简化方法。过去对这些系统的研究大多是在频域进行的，对稳定性特性的关注较少。然而，随着人们对时域可听化和虚拟传感的兴趣日益浓厚，保持稳定性的模型降阶对于高效时域仿真变得至关重要。此类系统的原始有限元模型已经很好地建立，但由于其高计算需求而没有扩展到时域。因此，本文提出了一种生成稳定降阶模型的方法。 Biot 模型的固体位移-总位移 () 公式用于描述多孔弹性介质。该公式得出一组具有无源传递函数的正对称系统矩阵。应用卡尔曼-雅库博维奇-波波夫引理和 Cholesky/LDL 分解，对该公式进行了修改，以满足先前证明的单侧模型降阶下的稳定性保持条件。此外，还研究了多孔弹性介质、空气和结构之间的耦合条件。最后表明，具有适当变量的耦合模型保持了稳定性保持特性。所提出的方法通过多次数值模拟得到验证。