TRANSIENT RESPONSE OF ONE-DIMENSIONAL DISTRIBUTED SYSTEMS: A CLOSED FORM EIGENFUNCTION EXPANSION REALIZATION

Abstract

The exact and closed form transient response of general one-dimensional distributed dynamic systems subject to arbitrary external, initial and boundary disturbances is determined. Non-self-adjoint operators characterizing damping, gyroscopic and circulatory effects, and eigenvalue-dependent boundary conditions are considered. Through introduction of augmented operators, a closed form modal expansion of the displacement and internal forces of the distributed system is derived. The eigenfunction expansion is realized in a spatial state formulation, which systematically yields exact eigensolutions, eigenfunction normalization coefficients and modal co-ordinates. The proposed method is illustrated on a cantilever beam with end mass, viscous damper and spring.