Size-Dependent Rigid–Flexible Coupling Dynamics of Functionally Graded Rotating Moderately Thick Microplates

Micro air vehicles, which are typical small-sized rotating-motion systems, have seen major advancements in recent years. To provide some theoretical basis for developing and producing micro air vehicles, this study establishes a novel rigid–flexible coupling dynamic model for functionally graded (FG) moderately thick rectangular microplates attached to a central rotating rigid hub based on the modified couple stress theory and first-order shear deformation theory. The proposed model incorporates nonlinear coupling term of in-plane deformation to reflect the dynamic stiffening effect caused by rotational motion. Material characteristics of the FG microplate have a linear power-law distribution along the thickness axis. Further, the discrete form dimensionless coupling dynamic equations and their numerical solutions are obtained by combining the Euler–Lagrange equation and the Chebyshev–Ritz method. Convergence and comparative studies are carried out to demonstrate the accuracy and validity of the proposed model. Thereafter, the influence of material length scale parameter, rotational speed, gradient index, and aspect ratio on the frequency of the microplates is investigated. Numerical results reveal that couple stress and dynamic stiffening effects both enhance the rigidity of the microplates, whereas the gradient index decreases the rigidity. Nonlinear coupling term which leads to significant differences in frequency value and trace line can’t be ignored for rotative structure. In-plane motion and its coupling terms play a significant function for the moderately thick or thick microplates. The increase of rotational speed and gradient index will reduce the size dependency of the microplate. Furthermore, the frequency trajectory steering and corresponding mode transition phenomenon are graphically represented.