Abstract
The spatial theory of elasticity is used to develop two variants of the semianalytic finite-element method for studying the frequencies of free vibrations and modes of distribution of displacements in them. The calculation by the two methods serves as a proof of the reliability of the analysis. The frequencies of free vibrations and the corresponding modes of distribution of displacements in a layered composite plate with two opposite boundaries free and the other two hinged are analyzed. A plate with a free lower surface, which is clamped to the lower surface and leaning on an elastic layer with finite thickness and inertial properties is considered. The high accuracy of the proposed models in these problems is demonstrated. It is pointed out that the inertial properties of the foundation should not be neglected.
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