RIGID-FLEXIBLE COUPLING DYNAMIC MODELING OF A ROTATING FUNCTIONALLY GRADED MATERIAL RECTANGULAR MINDLIN PLATE^1)

The rigid-flexible coupling dynamics of a functionally graded material rectangular plate with large overall motion is studied. Starting from the theory of continuum mechanics and based on the Mindlin plate theory, the meshless radial point interpolation method (RPIM) is used to discretize the deformation field of the rectangular plate. Considering the second-order nonlinear coupling deformation which is the longitudinal shortening caused by the transverse bending, the Lagrange equation of the second kind is used to derive the rigid-flexible coupling dynamics equation of the functionally graded material plate with large overall motion. The first-order approximate coupling model and the traditional zero-order approximate coupling model were used to simulate FGM cantilever plates at different speeds. The results show that the traditional zero-order model diverges and the first-order approximation model converges as the speed increases. The simulation results are compared with the assumed modal method and the finite element method to verify the correctness of the method in this paper and its superiority under the same calculation conditions. The effect of functional gradient index on the dynamic characteristics of a rotating functionally graded rectangular plate is studied. The results show that the lateral deformation of the plate increases and the natural frequency decreases as the functional gradient index increases, indicating that the increasing of the functional gradient index will increase the flexibility of the system. At the same time, the frequency loci veering phenomenon of the hub-FGM cantilever plate is discussed.