Model order reduction of time-domain vibro-acoustic finite element simulations with poroelastic materials

Cai, Yinshan, van Ophem, Sjoerd, Desmet, Wim and Deckers, Elke (2024) Model order reduction of time-domain vibro-acoustic finite element simulations with poroelastic materials. Computer Methods in Applied Mechanics and Engineering, 426, [116980]. (doi:10.1016/j.cma.2024.116980).

Abstract

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 (u ^s−u ^t) 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.

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Contributors

Author: Sjoerd van Ophem

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