MODAL COUPLING AND ACCURACY OF MODAL STRAIN-ENERGY METHOD

The modal strain energy (MSE) method is a technique for approximate an alysis of structures whose models in the frequency domain show frequen cy-dependent stiffness and damping matrices such as structures contain ing viscoelastic dampers. In this paper, the concept of modal coupling in the frequency domain is addressed and expressions for diagonalizab le frequency-dependent stiffness and damping matrices are given. The M SE method is described and the accuracy of this technique is investiga ted by computing the exact and approximate mean square responses of st ructures subjected to random excitation. Closed-form expressions of th e mean square error are obtained for single-degree-of-freedom systems with linear hysteretic and Maxwell-type damping and the accuracy of th e 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 t he MSE method for preliminary sizing of viscoelastic dampers is illust rated using a moment-resistant steel frame.