Free-wave propagation through combinations of periodic and disordered systems

Abstract

A method has been developed for the analysis of free-wave propagation through a combination of two different semi-infinite, monocoupled, periodic systems joined together without or through a finite periodic/disordered system. The general expressions derived from the analysis have subsequently been adapted to study the free flexural wave propagation in beam-type systems. Results have been computed and discussed for different combinations of beam systems which include semi-infinite periodic beams joined (i) through different periodic and disordered finite beams and (ii) without an additional beam at the junction. Attenuation of free waves in such systems, caused by six-span finite beam disorders, has been studied and compared to the attenuation of free waves in an infinite periodic beam and when one of its elements is different from the rest. Although multispan finite beam disorders generally attenuate the propagating incident waves, at certain discrete frequencies they offer no obstruction to such waves. The conditions under which this can happen have been identified and explained. It has been pointed out what type of finite disordered beams can be employed to prevent vibrational energy from flowing from one periodic system to another. The energy flow through the combined system, as governed by the transmitted free wave, has been discussed. The conditions have been explained under which two interacting attenuating flexural waves can transmit energy, although they are incapable of doing so individually.