Thermal buckling and free vibration analysis of rotating functionally graded (FG) graphene nanoplatelets (GNPs) reinforced nanocomposite porous metal-matrix microplates subjected to a linear thermal gradient are presented in this paper. The third-order shear deformation theory (TSDT) of Reddy and the Lagrange's equation of the second kind are adopted to derive the governing equations of motion via the modified couple stress theory (MCST). Different patterns of porosity distribution and GNPs dispersion are considered. The effective material properties of the microplate are determined by employing the Halpin-Tsai micromechanical model and rule of mixture. Galerkin method is chosen as a numerical technique, in which the comparison functions for displacements are approximately described as the boundary functions multiplied by Chebyshev polynomials, to solve the governing equations for various boundary conditions. The accuracy and effectiveness of the present results are validated by comparing with the previous literature. The effects of GNPs dispersion pattern, geometry and weight fraction as well as porosity coefficient, porosity distribution, angular velocity and material length scale parameter on the critical buckling temperature rise and fundamental frequency are studied. It is contrary to expectations that either increasing the amount of GNPs or increasing the porosity coefficient improves the thermal buckling behavior. Results also show that the GNPs' performances are affected not only by their geometry, but also by the centrifugally stiffening and small-scale effects. Rotating motion weakens the enhancement of GNPs on the thermal buckling behavior. More clamped boundaries enhance the critical buckling temperature rise and fundamental frequency. The outcomes of this work can be used as the reference for future applications in various fields of industry and technology.

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.

The free vibration of rotating functionally graded nanobeams under different boundary conditions is studied based on nonlocal elasticity theory within the framework of Euler-Bernoulli and Timoshenko beam theories. The thickness-wise material gradient variation of the nanobeam is considered. By introducing a second-order axial shortening term into the displacement field, the governing equations of motion of the present new nonlocal model of rotating nanobeams are derived by the Hamilton's principle. The nonlocal differential equations are solved through the Galerkin method. The present nonlocal models are validated through the convergence and comparison studies. Numerical results are presented to investigate the influences of the nonlocal parameter, angular velocity, material gradient variation together with slenderness ratio on the vibration of rotating FG nanobeams with different boundary conditions. Totally different from stationary nanobeams, the rotating nanobeams with relatively high angular velocity could produce larger fundamental frequencies than local counterparts. Additionally, the axial stretching-transverse bending coupled vibration is perfectly shown through the frequency loci veering and modal conversion.

A comprehensive model for vibration analysis of porous functionally graded (P-FG) rotating microplates under thermal environment is established within the framework of the first-order shear deformation theory (FSDT) and modified couple stress theory (MCST). Material properties of the microplates are temperature-dependent and alter through the thickness following a power-law function. The microplates with even porosity subjected to the nonlinear and uniform temperature rises are considered. The second-kind Lagrange's equations are employed for derivation of the governing equations of motion, which are numerically solved by the method of assumed modes constructing using the Chebyshev polynomials. The effectiveness and accuracy of the present approach are validated by the examples of convergence and comparison. A parametric study is performed to investigate the effect of angular velocity, material gradient index, material length scale parameter, temperature distribution, temperature rise, porosity index and thickness-to-length ratio on dimensionless nature frequencies for the rotating SSSS and CFFF P-FG microplates. Mode shapes for rotating P-FG microplates with different angular velocities are also presented. Numerical results show that the frequencies increase with increasing the angular velocity and material length scale parameter, while decrease with increasing the temperature rise and material gradient index. Results also indicate that the in-plane extension motions can be ignored in vibration analysis for the thin microplates, whereas play an important role for the moderately thick or thick microplates. The frequency loci veering phenomena and the mode shape conversions are displayed.