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Averaging the Equations of Small Oscillations in a Prestressed Randomly Inhomogeneous Medium / Goncharuk V.A. and Kukharenko Yu.A. // Vestnik Moskovskogo Universiteta. Seriya 1. Matematika. Mekhanika. 2010. № 1. P. 74-77 [Moscow Univ. Mech. Bulletin. Vol. 65, No 1, 2010]. The propagation of oscillations in anisotropic inhomogeneous media, such as granular materials and porous media, is studied theoretically near the regions with high initial stresses. An exact equation for the mean strains of such a medium is derived. The Feynman diagram technique developed in quantum field theory is used to treat the resulting infinite series. It is shown that the oscillation spectrum depends on the stress state of the medium under consideration.
Key words: nonlinear random inhomogeneous medium, diagram technique,
vibration spectrum.
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