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The class of plates with which this paper is concerned includes as an important special case plates consisting of two orthotropic sheets of equal thickness which are laminated in such a way that the axes of elastic symmetry enclose an angle +θ with the x, y-axes in one sheet and an angle −θ in the other sheet. For plates of this type there occurs a coupling phenomenon between in-plane stretching and transverse bending which does not occur in the theory of homogeneous plates and which has not been considered in earlier work for such plates. The general results of the present paper are illustrated by means of explicit solutions for two specific plate problems.

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A Kirchhoff-type theory is established for axisymmetric motions of heterogeneous isotropic circular plates. It is shown that a coupled extensional-flexural inertia term exists, in addition to the classical extensional and rotatory inertia terms. An analogy is found between the composite plate problem and the vibrations of homogeneous shallow spherical shells. The obtained sixth-order system of equations is solved in closed form in terms of Bessel functions, with an argument determined from a characteristic cubic equation. A transcendental frequency equation is then derived for a circular composite plate with clamped edge conditions. Numerous examples are studied, showing the significant effect of plate heterogeneity on its vibrational response. Possibility of composite systems to transcend the frequencies of the individual constituents is clearly indicated by the theoretical results and checked experimentally.