Size-dependent vibrations of porous functionally graded rotating microplates under thermal environment

Abstract

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.