Free vibration of transversely isotropic circular plates

A three dimensional solution to study the nonaxisymmetric free vibration of transversely isotropic circular plates is discussed. As circular and annular plates are extensively used in various engineering applications and the associated dynamic studies. Exponential functions are used to get three dimensional solutions of these problems in which hyperbolic sine and cosine functions are employed. The symmetric mode vibration and the antisymmetric mode vibration, with respect to the middle plane of the plate, can be separated in the case of the out-of-plane vibration. The vibration mode shapes provide important information for design of electric devices as well as engineering structures. The frequency equation are found which implies the corresponding vibration mode is antisymmetric with respect to the middle plane, thus determine the natural frequency of the antisymmetric out-of-plane vibration of circular plane.