Free Vibration Analysis of Rotating Mindlin Plates with Variable Thickness

Abstract

The modal analysis of rotating cantilevered rectangular Mindlin plates with variable thickness is studied. The Ritz method is used to derive the governing eigenfrequency equation by minimizing the energy functional of the plate. The admissible functions are taken as a product of the Chebyshev polynomials multiplied by the boundary functions, which enable the displacements and rotational angles to satisfy the geometric boundary conditions of the plate. The Chebyshev polynomials guarantee the numerical robustness, while the Ritz approach provides the upper bound of the exact frequencies. The effectiveness of the present method is confirmed through the convergence and comparison studies. The effects of the dimensionless rotational speed, taper ratio, aspect ratio and thickness ratio on modal characteristics are investigated in detail. The frequency loci veering phenomenon along with the corresponding mode shape switching is exhibited and discussed.