Surface acoustic wave in layered bimodule medium with amplitude-dependent behavior
Moscow state University named after M. V. Lomonosov, Faculty of physics, Department of acoustics, Russia, 119991, Moscow, Leninskie Gory, MGU, tel. (495)-9392943, firstname.lastname@example.org
It is well known that localized acoustic disturbances such as Rayleigh and other types waves propagate along the interfaces of layered media. These waves have sufficient energy and less geometric divergence compared to bulk waves. Given the strong dependence of the localization depth of the wave from its length it allows the use of these waves for diagnostics of medium in the problems of geophysics and nondestructive testing. The greatest interest is associated with the study of inhomogeneous media with complex internal structure. In addition to the study of inhomogeneities of usual form (density, sound velocity, etc.) in recent years an increasingly urgent problem has become in the study of structural and nonclassical ihhomogeneities and nonlinearities of medium. For example, pores or cracks can be present, which has a complex dynamics. It is clear that in the presence of cracks, the behavior of medium will be different in phases of expansion and contraction. For tensile cracks just a small effort, and for its compression, on the contrary, one need more power. The simplest model is a bimodule medium with different modules of elasticity in compression and in tension. A more complex analogue of this model is the medium in which the elasticity modulus changes at some critical value of the driving amplitude. This means that, for example, medium contains some internal structure. When exceeding the critical value of the driving amplitude the response of this structure turns on or the destruction of this structure matter that leads to changes in elastic moduli. For example, in polymer media may occur rupture of the polymer chains.
In this work the structure of the surface waves is investigated formed in the bimodule medium, modeling the fractured rock. The constitutive equations for such media are set up. Equations describing the surface acoustic waves propagation are derived. In fact, this medium is nonlinear, which means the distortion of the wave profile, while for each interval of amplitudes equations are linear. Temporal profiles of the non-linear distorted waves and their spatial structure are calculated, dispersion relations are determined. It is shown that the wave localization depth significantly changes. the possibility of recovery of medium parameters from acoustic measurements is analyzed. The generalization of the model to the case of bimodule medium with the change of the elastic moduli at the critical amplitude of external influence is done.
This work was supported by RFBR grant No. 16-02-00764.