Time integration of finite element models with nonlinear frequency dependencies

TL;DR

This paper introduces a novel method for linearizing finite element models with nonlinear frequency dependencies, enabling more accurate time-domain simulations of sound and vibrations with frequency-dependent damping properties.

Contribution

The paper presents the Extended AAA method, combining classical AAA with polynomial terms and filtering to linearize frequency-dependent finite element models for time-domain analysis.

Findings

Effective linearization of frequency-dependent models achieved.

Enhanced stability through pole filtering.

Applicable to transient sound and vibration simulations.

Abstract

The analysis of sound and vibrations is often performed in the frequency domain, implying the assumption of steady-state behaviour and time-harmonic excitation. External excitations, however, may be transient rather than time-harmonic, requiring time-domain analysis. Some material properties, e.g.\ often used to represent for damping treatments, are still described in the frequency domain, which complicates simulation in time. In this paper, we present a method for the linearization of finite element models with nonlinear frequency dependencies. The linearization relies on the rational approximation of the finite element matrices by the AAA method. We introduce the Extended AAA method, which is classical AAA combined with a degree two polynomial term to capture the second order behaviour of the models. A filtering step is added for removing unstable poles.