Free Vibration Analysis of Rotating Cantilever Flexible Plates Using the p-Version of the Finite Element Method

摘要

A p-version of the finite element method is applied to free vibration analysis of rotating cantilever plates in conjunction with the new modeling dynamic method using the arc-length stretch deformation. The flexible and the rigid body DOF are supposed uncoupled, the linear equations of motion are derived including coupled terms between the in-plane and the transverse bending vibration, caused by the gyroscopic effect. The hybrid displacements may be expressed as the combination of the in-plane and out-of-plane shape functions formulated in terms of linear and cubic polynomials functions used generally in FEM plus a variable number of trigonometric shapes functions representing the internals DOF for the plate element. Trigonometric enriched stiffness, mass, gyroscopic and centrifugal stiffness matrices are derived using symbolic computation. The convergence properties of the rotating plate Fourier p-element proposed and the results are in good agreement with the work of other investigators. The influences of rotating speed and coupling effect on the natural frequencies are investigated. It is shown that by this element the order of the resulting matrices in the FEM is considerably reduced leading to a significant decrease in computational effort.