Three-Dimensional Vibrational Characteristics of Functionally Graded Rotating Microbeams Based on the Higher-Order Refined Shear Deformation Theory

Abstract

This study establishes a novel three-dimensional dynamic model for functionally graded rotating microbeams simultaneously considering flapwise and chordwise shear effects based on a refined shear deformation theory and the modified couple stress theory. Five kinematic variables are introduced to describe the rotating microbeam’s axial, flapwise, and chordwise motions using a higher-order refined shear deformation theory. The related strain energy and kinetic energy functionals are discretized by the assumed mode method. Applying the Euler–Lagrange variational formulation, the governing equations for the rotating microbeam are obtained. Selective examples are provided to demonstrate the convergence and effectiveness of the proposed model. Finally, the impacts of slenderness ratio, rotation speed, material index, material length scale parameter (MLSP), and Poisson’s effect on the vibrational characteristics of the microbeam are examined. Numerical results indicate that the mode shape transition and frequency loci veering phenomena could easily occur under slight changes in the above factors when dense modes appear in the rotating microbeam; moreover, there is a positive/negative competitive relationship among the effects of rotation speed, MLSP, and shear deformation; Poisson’s effect seriously affects the coupling between axial and non-axial motions of the rotating microbeam. The results obtained are expected to provide data accumulation and methodological basis for the failure analysis and vibration shape determination of micro air vehicles.