A hierarchy of approximate elastodynamic plate theories is deduced from the three-dimensional equations of elasticity. The derivation is based upon asymptotic expansions in a parameter viewed as the ratio of plate half thickness to a dominant signal wavelength of motion. Approximate theories of any desired order of accuracy are contained in a single compact set of partial differential equations with the order of approximation determined by the order of truncation of the differential operators appearing in the equations. As examples, particular cases of free extensional and forced flexural vibrations are studied. Lower-order theories for these cases are compared to some existing approximate theories of the same order.

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