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Plate vibrations with periodically changing parameters

Vibrations of square plate with periodically changing parameters are considered. The averaged fourth-order partial differential equation for the plate deflection w is offered. Solution of the problem is obtained by using the approximate theory. The approximate results are presented by analytical formulas. Asymptotic averaging (realized in Wolfram Mathematica) and Finite Elements Method (ANSYS) are used to get the values of vibrations frequencies. The comparison of numerical and asymptotic results is performed.