STOCHASTIC-MODEL FOR WAVE LOCALIZATION IN ONE-DIMENSIONAL DISORDERED STRUCTURES

This paper presents a probabilistic study of the effects of structural irregularity on wave propagation along an infinite 1-D chain. A gener al integral equation method based on Markov chain theory is used to de termine the phase probability density function (pdf) at the scatterers distributed irregularly along the chain. The scatterers could be atom s in a one-dimensional crystal, or ribs on a flat plate or membrane. T he integral equation derived for the phase pdf is simplified considera bly when the scatterers are distributed completely randomly or quasi-p eriodically. In these cases, the integral equations may be asymptotica lly solved for the phase density functions in the limit of weak or str ong scattering; the localization factors are then obtained. The presen t approach is quite general and is directly applicable to any disorder ed one-dimensional system consisting of identical scatterers that are arranged according to a probability distribution function. The validit y of the present asymptotic solutions is examined and verified by comp aring against the existing analytical solutions for simple atomic or m echanical disordered systems. (C) 1998 Acoustical Society of America. [S0001-4966(98)00402-0].