Y. Yang et Dm. Photiadis, STOCHASTIC-MODEL FOR WAVE LOCALIZATION IN ONE-DIMENSIONAL DISORDERED STRUCTURES, The Journal of the Acoustical Society of America, 103(2), 1998, pp. 751-759
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].