Active and Passive Vibration Damping

5Finite Element Modeling of Viscoelastic Damping by Modal Strain Energy Method

5.1 Introduction

The modal strain energy (MSE) method has been widely accepted as an effective and practical means for predicting the modal parameters of complex structures treated with viscoelastic damping treatments. The method is based on estimating the modal strain energies of the structure and the viscoelastic material (VEM) by using the undamped (real) mode shapes of the structure/VEM assembly instead of the exact damped (complex) mode shape. Such an approximation makes it easy to integrate the MSE with commercial finite element codes that generally do not use complex eigenvalue problem solvers. The theoretical basis of the original MSE method and several of its modified versions are presented. Application of the method to various types of viscoelastic damping treatments is discussed and compared with the predictions obtained by using the exact complex eigenvalue problem solvers and the Golla–Hughes–McTavish Model (GHM) approach discussed in Chapter 4.

5.2 Modal Strain Energy (MSE) Method

The MSE method was originally introduced by Kerwin and Ungar (1962) and then extended by Johnson and Kienholz (1982) as an approximate means for predicting the modal parameters of complex structures treated with viscoelastic damping treatments. The method is based on describing the viscoelastic material by the “complex modulus” approach and therefore, it is limited to frequency domain analysis. To account ...