Active and Passive Vibration Damping

4Viscoelastic Materials

4.1 Introduction

Classical models of viscoelastic materials (VEMs), such as those by Maxwell, Kelvin–Voigt, Poynting and Thomson, and Zener, have been shown in Chapter 2 to have serious limitations in modeling accurately the behavior of realistic VEMs. Furthermore, the use of the classical approach of the complex modulus to represent the dynamics of VEMs is limited to frequency domain analysis. To avoid such limitations of these classical models and approaches, several advanced models of the VEMs have been developed. These include: Fractional Derivative (FD) model (Bagley and Torvik 1983), Golla–Hughes–McTavish (GHM) model (Golla and Hughes 1985), and the Augmented Temperature Fields (ATF) (Lesieutre and Mingori 1990).

In this chapter, considerable effort is devoted to present the merits and limitations of these models because of their wide and ease of use in the analysis of damped structures. Particular emphasis is placed on integrating the models with finite element models simulating the dynamics of structures treated with VEMs. Such integration is essential to the prediction of the response of these structures both in the time and frequency domains. This enables the computation of the structural response to transient, shock, as well as sinusoidal loading.

4.2 Golla–Hughes–McTavish (GHM) Model

The GHM model was developed by Golla and Hughes in 1985. The model describes the shear modulus of VEMs with a second order differential equation unlike the ...