Modal Coupling and Accuracy of Modal Strain Energy Method

Abstract

The modal strain energy (MSE) method is a technique for approximate analysis of structures whose models in the frequency domain show frequency-dependent stiffness and damping matrices such as structures containing viscoelastic dampers. In this paper, the concept of modal coupling in the frequency domain is addressed and expressions for diagonalizable frequency-dependent stiffness and damping matrices are given. The MSE method is described and the accuracy of this technique is investigated by computing the exact and approximate mean square responses of structures subjected to random excitation. Closed-form expressions of the mean square error are obtained for single–degree-of-freedom systems with linear hysteretic and Maxwell-type damping and the accuracy of the MSE method in the estimation of response of multi–degree-of-freedom structures with nonclassical, hysteretic, and Maxwell-type damping is investigated using a simple base-isolated model. Finally, the use of the MSE method for preliminary sizing of viscoelastic dampers is illustrated using a moment-resistant steel frame.