Abstract
The paper is devoted to construction of refined hyperbolic models of plates and shells predicting the wave propagation with the finite velocities unlike the classical Kirchhoff plate theory and Kirchhoff-Love shell theory and other known modifications of parabolic type. It is shown that these refined models can be obtained as mathematical approximations of the original hyperbolic model of elastodynamics without introducing some additional corrections of physical kind unlike widely used refined phenomenological theories of Timoshenko-Mindlin plates (1951), Herrmann-Mirsky, Lin-Morgan, Naghdi-Cooper shells (1956) and others. From the point of view of the spectral theory, any theories of plates and shells are of approximate kind and, as a result, deal with a finite number of eigenvalues and wave modes instead of infinite numbers of eigenvalues corresponding to exact elastodynamic problem.
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