Theory of propagation of elastic waves in nonhomogeneous media

Abstract

1. The effective tensor operator of the wave equation of ideally disordered composites is an integrodifferential tensor operator containing terras with second derivatives with respect to the coordinates and time and mixed second-order derivatives. The kernels of the spectral operators on which the named differential operators act are components of tensors of the fourth, second, and third rank. Their dependence on the coordinates is determined by the specific form of the binary correlation functions of the material constants. 2. General formulas for the scattering coefficient and phase and group velocities of propagation of longitudinal and transverse waves can be obtained by using the Burre approximation, an exponential coordinate relation for the binary correlation functions, and the notion that the mean field in the composite, in the form of a monochromatic wave, is characterized by the effective wave vector. 3. Analytic expressions were obtained for one longwave and two shortwave asymptotes of the investigated parameters. It was shown that these asymptotes coincide with the literature data in the longwave case and are confirmed by experimental results in the shortwave case.