Free vibration analysis of rotating thick plates

A finite element formulation for vibration analysis of rotating thick plates is developed. Mindlin plate theory combined with second order strain–displacement assumptions are applied for plate modeling. Kane dynamic method is employed for the derivation of nonlinear governing equations of motion, which include Coriolis effects and the couplings between in-plane and out of plane deformations. The nonlinear equations of motion are linearized using the conventional quasi static method and frequency results are obtained. The effects of different parameters including aspect ratio, thickness ratio, hub radius ratio and rotation speed on dimensionless natural frequencies are investigated and discussed. In addition, the differences between linear and nonlinear approaches toward in-plane vibration analysis of rotating plates are studied. Tune speeds are observed for the in-plane vibration frequencies. The results are in good agreement with those of other theories and experiments.