Axisymmetric Vibrations of Isotropic Composite Circular Plates

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.