Simulation of combined systems by periodic structures: the wave transfer matrix approach

An exact closed-form method is presented for frequency domain analysis of linear uniform combinedsystems. The proposed method is based on the idea that such systems can be treated as if they were periodic structures under multiple excitations. In other words, the continuous system is viewed as subdivided into small equispaced subsystems so that all the arbitrarily located point-wise discontinuities (i.e., external and boundary disturbances, forces exerted by constraints and attached discrete systems) appear as acting at subsystem interfaces. By adapting the periodic structure wave solution, the response of the combinedsystem is found to be formed by afree wave fieldincorporating the dynamics of the entire system and aforced wave fieldgenerated by discontinuities in both directions, as if the system were infinite in extent. In order to validate the theory, two examples are considered. In the first example, the phase closure principle is invoked to predict the free and forced motion of a translating string constrained by arbitrarily spaced linear springs. In the second example, formulas for natural frequencies of beams on multiple constraint supports with different boundary conditions are obtained from those of beams with simply supported ends.