Steady‐State and Transient Responses of Linear Structures

A simple, computationally efficient procedure is presented with which the steady‐state response of a discrete linear system to a periodic excitation may be computed from an analysis of its transient response over a single cycle of the excitation. The procedure also is adapted to the solution of the inverse problem, i.e., to evaluate the transient response of the system from knowledge of its steady‐state response to a periodic extension of the excitation. The procedures are introduced by reference to single degree of freedom systems. They are then extended to multi‐degree of freedom systems for which the modal superposition method of analysis is applicable, and are illustrated by a series of simple examples. Both undamped and viscously damped systems are considered.