UNIAXIAL WAVES IN RANDOMLY HETEROGENEOUS ELASTIC MEDIA

Propagation of uniaxial sound waves in heterogeneous linear elastic on e-dimensional media is considered. The scalar wave equation is transfo rmed by the Liouville substitution and the Dyson integral equation is applied for a statistically homogeneous field of heterogeneities that results in an integral spatial representation for the mean wave field. The mean field is analysed in detail for the following three correlat ion functions: (i) an exponential one; (ii) a mean-square differentiab le correlation function with a hidden periodicity; and (iii) a nondiff erentiable correlation function with a hidden periodicity. Despite the variety of the stochastic properties of the media, the equation for t he mean field takes formally the same form for the three cases. For th is reason, the general case of the random elastic medium with an arbit rary heterogeneity of small scale is considered and simple closed form expressions for the mean field and attenuation are derived. Applicabi lity of the modelling of extended complex engineering structures by on e-dimensional random media is discussed. The overall mechanical parame ters of the primary structure and the secondary systems determine aver age rigidity, average mass density and average wave speed, while the s econdary systems determine the attenuation. The latter is shown to dep end upon the size and range of the secondary systems. (C) 1997 Elsevie r Science Ltd.