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 combined systems. The proposed method is based on t he idea that such systems can be treated as if they were periodic stru ctures under multiple excitations. In other words, the continuous syst em is viewed as subdivided into small equispaced subsystems so that al l the arbitrarily located point-wise discontinuities (i.e., external a nd boundary disturbances, forces exerted by constraints and attached d iscrete systems) appear as acting at subsystem interfaces. By adapting the periodic structure wave solution, the response of the combined sy stem is found to be formed by a free wave field incorporating the dyna mics of the entire system and a forced wave field generated by discont inuities 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 f ree and forced motion of a translating string constrained by arbitrari ly spaced linear springs. In the second example, formulas for natural frequencies of beams on multiple constraint supports with different bo undary conditions are obtained from those of beams with simply support ed ends. (C) 1998 Academic Press Limited.