ABSTRACT
In linear elasticity if one uses quasi-finite element formulation in space based on GM/WF $ {\text{GM/WF}} $, then the following system of ordinary differential equations (ODEs) in time is obtained for the discretization in space. This chapter describes the mode superposition method which can be effectively used to obtain time response or transient dynamic response of a system subjected to time-dependent excitations. It summarizes the details for obtaining transient response using natural modes for undamped system. The chapter then considers transient dynamic response of systems in which damping cannot be neglected. The mode superposition technique of obtaining transient dynamic response of a large discretized system using finite elements in space is particularly effective if one assume proportional damping. The chapter also provides some general remarks regarding modal basis, time integration, and theoretical solutions of decoupled equations for linear structural dynamics.
