Free Vibration of Circular Plates with Various Edge Boundary Conditions by 3-D Elasticity Theory

Free vibration of transversely isotropic circular plates with various edge boundary conditions is analyzed on the basis of theory of elasticity without a priori plate assumptions. The governing equations for vibration of transversely isotropic circular plates are derived from the three-dimensional equations of elasticity in the cylindrical coordinates. By means of separation of variables, two sets of solutions are obtained, which enable us to satisfy various edge boundary conditions of the problems and determine the natural frequencies of the circular plates. Numerical results for three kinds of edge conditions are evaluated and compared with those obtained according to 2D plate theories such as DQM, HSDT and Mindlin's solutions. The study shows that our results can find much more natural frequencies of circular plates than the 2D solutions for circular plates. These 2D solutions are applicable while the ratios of thickness to radius of the plates are lesser than 0.05 and the edge conditions are clamped or simply- supported.