Wave Propagation in Periodic and Disordered Layered Composite Elastic Materials.

摘要

A powerful complex transfer matrix approach to wave propagation perpendicular to the layering of a composite of periodic and disordered structure is worked out showing propagating and stopping bands of time-harmonic waves and the singular cases of standing waves. A state ratio of left- and right-going plane waves is defined and interpreted geometrically in the complex plane in terms of fixed points and flow lines. For numerical considerations and extension of the approach to higher dimensional problems a continued fraction expansion of the state ratio mapping is presented. Impurity modes of wave propagation in composites with widely spaced impurity cells of different elastic materials are discussed. Stopping bands in the frequency spectrum of global waves in fully disordered composites are found to exist in the range of frequencies corresponding to common gaps in the spectrum of constituent regular periodic composites which are constructed from the cells of the disordered system. For those frequencies, waves propagate only a (short) finite distance and are therefore strongly localized modes in a composite of fairly large extent. (Author)