Micro temperature-dependent FG porous plate: Free vibration and thermal buckling analysis using modified couple stress theory with CPT and FSDT

For the first time in this paper, free vibration and thermal buckling of micro temperature-dependent FG porous circular plate subjected to a nonlinear thermal load are numerically studied. The governing equations are derived based on Hamilton's principal and using both classical and the first-order shear deformation theories in conjunction with the modified couple stress theory. Generalized Differential Quadrature method is applied to solve the equations with associated boundary conditions. The results reveal that the increase of size dependency and the temperature-change would lead to the increase of differences between the first natural frequencies predicted based on the two theories. In contrast, the porosity and the FG power index do have not any effect on that. While the effect of porosity on free vibration of clamped and free plates are negligible, but the effect of porosity for hinged ones is considerable as the temperature-change increase. Moreover, the critical conditions of the plates which are expressed by porosity, FG power index, size dependency, temperature-change and geometrical dimensions are presented, as well. Numerical results are in good agreement with those available in literature in some special cases.