Abstract
A systematic formulation of the theory of transverse and longitudinal vibrations of “thin” plates of thickness 2h is presented. Transient processes are described by the theory. The paper is devoted mainly to the derivation of equations for the dynamics of an elastic layer with finite phase velocities of all harmonics in Fourier integral representation of the solutions of the elasticity equations for the vectors of displacements u and normal stresses σz = σ, where the subscript z refers to the normal coordinate. The results are compared with existing Timoshenko-type two-parameter theories of flexural and longitudinal vibrations of beams, and new aspects of the physical processes in plates far from the edge surface of the plate are brought to light.
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