Free transverse vibrations of the multilayered rectangular plate are considered. The composite plate consists of 2n orthotropic layers symmetrically located about the midplane, where the central (n and n+1) layers are piezoelectric polymer. Using the Rayleigh method, closed formulas are obtained for the frequencies of flexural vibration. A generalized frequency expression is presented in terms of definite integrals containing the characteristic functions. Formulas for evaluating these integrals for common types of boundary conditions are available in the literature. In particular, an expression is derived for the resonance frequencies of the completely free composite piezoelectric polymer plate.
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Donald Ricketts (1985) studied this question.
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