Free vibration of circular and annular plates with variable thickness and different combinations of boundary conditions

In this paper, the first nine frequency parameters of circular and annular plates with variable thickness and combined boundary conditions are computed for different thickness to radius ratios. Several combined boundary conditions are considered for inner and outer edges. These are free, soft and hard simply supported, and clamped boundary conditions. Three-dimensional elasticity theory is used. Results of this paper are compared with works of other authors and the results of finite element method analysis which are in agreement. Data for thick circular and annular plates with linear and parabolic thickness variation and different combinations are presented for the first time.