Complex Eigenvalue Analysis for Structures with Viscoelastic Behavior

TL;DR

This paper introduces a method for eigenvalue analysis of structures with multiple viscoelastic materials, using a reduced state-space formulation to efficiently identify all materials with shared time-constants.

Contribution

It proposes a novel approach to simultaneously identify multiple viscoelastic materials with shared time-constants, reducing the size of the eigenvalue problem significantly.

Findings

Effective reduction of state-space size

Accurate mass and stiffness operator reduction

Enhanced modal basis for improved results

Abstract

This document deals with a method for eigenvalue extraction for the analysis of structures with viscoelastic materials. A generalized Maxwell model is used to model linear viscoelasticity. Such kind of model necessitates a state-space formulation to perform eigenvalue analysis with standard solvers. This formulation is very close to ADF formulation. The use of several materials on the same structure and during the same analysis may lead to a large number of internal states. This article purpose is to identify simultaneously all the viscoelastic materials and to constrain them to have the same time-constants. As it is usually possible, the size of the state-space problem is therefore widely reduced. Moreover, an accurate method for reducing mass and stiffness operators is proposed; The enhancement of the modal basis allows to obtain good results with large reduction. As the length of the paper is limited, only theoretical development are presented in the present paper while numerical results will be presented in the conference.