There is proposed a method of studying wave processes in locally nonhomogeneous solids with account for geometrically non-uniform surface. The method is based on the equation system of the locally nonhomogeneous elastic solid model obtained within the local gradient approach and the use of averaging operation to separate oscillatory and slowly variable over period of oscillation components of displacement and density fields.

At the example of a layer there is illustrated an application of the method to study the frequencies of natural oscillations for different fixing conditions at the layer surfaces. It was established that the dependence of frequencies of natural oscillations of the layer on the characteristic sizes the nearsurface and structural nonhomogeneities in the case of the free layer surfaces is much higher comparing to the fixed surfaces case.

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