Nonlinear dynamic analysis of damped structures using the transfer matrix technique

Abstract

A conceptually simple and computationally efficient numerical model, based on the transfer matrix formulation is proposed for the prediction of nonlinear dynamic responses of a coupled shear wall structure incorporating damping. With the transfer matrix method, damping is introduced into the formulation through the field and station transfer matrices using the constitutive law. The effect of damping on the responses of a vibrating beam is incorporated into the station transfer matrix while those of the walls are incorporated into the field transfer matrix. The nonlinear behaviour is approximated as a sequence of successively changing linear systems over a short time interval. The transfer matrix formulation adopts established models of material behaviour in dealing with the inelastic beam element deformation and load reversals. The dynamic solution assumes constant properties within short time increments, and relies on the kinematic relationships of the Wilson θ method.