Elastic–Viscoelastic Composite Structures Analysis With an Improved Burgers Model

Abstract

Composite structures integrated with viscoelastic materials are becoming more and more popular in the application of vibration suppression. This paper presents a comprehensive approach for analyzing this class of structures with an improved Burgers model, from material constitutive modeling, finite element formulation to solution method. The refined model consists of a spring component and multiple classical Burgers components in parallel, where the spring component converts the viscoelastic fluid model to a viscoelastic solid model and the multiple Burgers components increase the accuracy. Through the introduction of auxiliary coordinates, the model is applied to the finite element formulation of composites structures with viscoelastic materials. Consequently, a complicated Volterra integro-differential equation is transformed into a standard second-order differential equation and solution techniques for linear elastic structures can be directly used for elastic–viscoelastic composite structures. The improved Burgers model is a second-order mini-oscillator model, in which every mini-oscillator term has four parameters. The model parameters determination is performed by optimization algorithm. By comparison of model fitting results for a typical viscoelastic material, the refined model is better in accuracy than Golla–Hughes–McTavish (GHM) model and original Burgers model. Finally, several numerical examples are presented to further verify the effectiveness of the improved Burgers model.