Modified couple stress-based free vibration and dynamic response of rotating FG multilayer composite microplates reinforced with graphene platelets

A centrifugally stiffened size-dependent model is developed for dynamic analysis of rotating functionally graded (FG) multilayer composite microplates reinforced with graphene platelets (GPLs) based on the modified couple stress theory and the first-order shear deformation theory. The effective elastic modulus of the graphene platelet-reinforced composite (GPLRC) is calculated on the basis of the modified Halpin–Tsai model, while a rule of mixture is adopted to predict the effective mass density and Poisson’s ratio. The second-kind Lagrange’s equations are employed to derive the governing equations of motion, in which the mode functions for displacements are constructed by Chebyshev polynomials multiplied by the boundary functions. The free vibration problem is determined by a complex modal analysis based on the state space method, and the dynamic responses under prescribed rotational motions are calculated by the fourth-order Runge–Kutta–Merson’s method. The convergence and comparative examples are carried out to validate the effectiveness and accuracy of the proposed model. A parametric study is conducted to investigate the effects of material length scale parameter, hub radius ratio, angular velocity, GPL weight fraction, distribution pattern and geometry property on the dynamic behaviors of the rotating FG GPLRC simply supported and cantilevered microplates. Numerical results show that the rotational motion and size dependency significantly affect the reinforcement effect of GPL. Results also indicate that the dispersion of the square GPLs with fewer graphene layers and larger contact surface area near the bottom and top positions can reinforce the stiffness more effectively.