Buckling and free vibration of the FGM thin micro-plate based on the modified strain gradient theory and the spline finite strip method

In the present article the mechanical instability and free vibration of FGM micro-plate based on the modified strain gradient theory were studied using the spline finite strip method. By daily increase in the application of micro-scale structures, developing theories were become essential to account in a way for the size-reduction effect. The modified strain gradient theory based on three length scale parameters, has the capability of evaluating structures at the micro size level. Considering the obtained results, it was clear that increasing the length-scale parameter would increase the critical buckling load and the vibration frequency, similar to the macroscopic case. In addition, increasing the power of volume fraction module decreases the critical load and the natural frequency of micro plate. Finally, the effect of length-scale parameter, boundary conditions, volume fraction module and dimensions of the micro-plate on critical loading and natural frequency of micro-plate were studied.