Free vibration frequencies of a circular thin plate with variable parameters

Transverse vibrations of an inhomogeneous circular thin plate are studied in the paper. Nondimensional equations based on Kirchhoff - Love hypotheses describing nonaxisymmetric vibrations of inhomogeneous plate are derived. Using the perturbation method, asymptotic formulas are obtained for the free vibration frequencies of a plate, whose thickness and Young's modulus linearly depend on the radial coordinate. The influence of the plate edge conditions on the frequencies and the behavior of frequencies for a plate with the fixed mass are analyzed. For the lower free vibration frequencies the results of asymptotic and finite elements analyses are compared.