Exact Solutions for Axisymmetric Vibration of Laminated Circular Plates

Abstract

Based on fundamental equations of three‐dimensional elasticity and giving up any assumptions about displacement models and stress distribution, the state equations for the axisymmetric free vibrations of transversely isotropic circular plates are established. Because the four quantities appearing in the state equations happen to be the compatibility quantities of the interfaces, it is extremely convenient to develop the state equations of laminated circular plates with transversely isotropic layers. The exact solutions for such problems with simply supported and clamped edges are presented in this paper. Every fundamental equation of three‐dimensional elasticity can be exactly satisfied and all five elastic‐flexibility constants can also be taken into account by the present method. No matter how many layers are considered, the calculation always leads to solving a set of linear algebraic equations of the second order. Numerical results are obtained and compared with the results calculated using the Reissner and Mindlin theories, respectively.