Short notes

Averaging the equations of small oscillations in a prestressed randomly inhomogeneous medium

V. A. Goncharuk^a, Yu. A. Kukharenko<sup>b

a</sup> Lomonosov Moscow State University, Faculty of Mechanics and Mathematics
^b Institute of Physics of the Earth, Russian Academy of Scienses

Abstract: This paper is concerned with the theoretical study of vibration propagation in anisotropic stochastic inhomogeneous media such as granulated material and porous media, in the area of high initial tension. An exact equation for the mean deformation of media is derived. The Feynman diagram technique developed in quantum field theory is used to deal with appeared infinite series. A stress dependence of the vibration spectrum is shown.

Key words: nonlinear random inhomogeneous medium, diagram technique, vibration spectrum.

UDC: 534-18

Received: 16.03.2009