Free vibration frequencies of a circular thin plate with variable parameters (Q2227912)

Transverse vibrations of an inhomogeneous thin circular plate is studied in this paper. The authors have used the perturbation method and have obtained asymptotic formulas for free-vibration frequencies of a plate whose thickness and Young's modulus linearly depend on radius. The dependence of thickness of the plate on its radius is assumed to be linear. Similarly, the dependence of Young's modulus of the plate's material on radius is assumed to be linear. The effect of the boundary conditions on frequencies and the behavior of frequencies for a plate with the fixed mass are analyzed. For lower frequencies of the plate, the asymptotic results are compared with the results of analysis by finite elements. Using the asymptotic formulas obtained in this work, it is possible to find good approximations for the natural vibration frequencies of plates in the case of a relatively small linear change in the thickness parameters and Young's modulus. In reviewer's opinion, there is a need to analyse the numerical results more rigorously with regard to their accuracy.