Stable model order reduction for time-domain exterior vibro-acoustic finite element simulations

Abstract

This paper presents a novel method that enables model order reduction of a fully-coupled, exterior vibro-acoustic finite element model for time domain simulations. The method preserves the stability of the full model and reduces the amount of degrees of freedom significantly, with only a moderate amount of calculation complexity. Infinite elements are used on the finite element boundary to satisfy the Sommerfeld radiation condition. Two different strategies to calculate the reduced order model are compared. The first strategy works with a split reduced basis and can be applied on any fully stable model. The second strategy starts from a modified Everstine formulation and directly builds a reduced basis from the full model, leading to more compact reduced order models. Furthermore, a method is derived to perform explicit time integration on the reduced system, while avoiding the inversion of the mass matrix, which might not be possible due to the presence of the infinite elements. Also this method is shown to preserve the stability of the model and a computationally efficient way for implementation of the method is discussed. The effectiveness of the novel methodology is demonstrated with two numerical models.

A Benchmark Study on Eigenfrequencies of Fluid-Loaded Structures

“…The reduced second-order system of Eq. (2.10) is generated in the same manner as proposed by van Ophem, 3 i.e. using the SOAR algorithm in order to generate an unsplit orthonormal projection basis V. An arbitrary initialization vector with random values between 0 and 1 is chosen for the generation of the projection basis.…”

“…By this, one accounts for the actual zero-block of the mass matrix of the IFEM domain M e , as proposed by van Ophem. 3 The projection process leads to fully-populated, dense system matrices of the reduced system. The reduced quadratic EVP is solved efficiently with the open-access MATLAB function quadeig.…”

Automatic and Sampling-Free Parametric Model Order Reduction of Vibro-Acoustic Systems

“…This is done to preserve the definiteness properties of the full order system matrices, such that stability is preserved. For vibro-acoustic systems it has been shown how the use of a one-sided projection, in combination with a specific system formulation, leads to stability preservation [5]. Thus, both of the above approaches will lead to stable ROMs when the full order system is stable, a onesided projection is used, and the correct system formulation is used.…”

“…The application of MOR on vibro-acoustic systems comes with specific challenges, such as time-stability and the modeling of parametric variations that are related to the physical system, such as structural boundary conditions, a change of material properties, etc [5]. Recently, a novel reduction scheme for lowrank parametric variations in vibro-acoustic systems was derived [1], using earlier derived techniques for first order system as starting point [6], [7].…”

3 Case studies of model order reduction for acoustics and vibrations

“…Keeping the system in u-p formulation necessitates the use of an extended projection basisṼ, resulting in a ROM with possibly up to twice as many degrees of freedom. This ROM approach was recently extended towards time-stable coupled exterior vibro-acoustic finite element simulations [55].…”