Bending, Buckling and Vibration Analysis of Complete Microstructure-Dependent Functionally Graded Material Microbeams

A new functionally graded non-classical Timoshenko microbeam model is developed by using a variational formulation. The new model incorporates strain gradient, couple stress (rotation gradient) and velocity gradient effects and explains a power-law variation of two-phase materials through the thickness direction. The new model contains three additional material constants to account for the relative three gradient effects. The static bending, buckling and free vibration problems of the newly developed functionally graded material (FGM) beam are then analytically solved. Numerical results show that the differences between the prediction results of the current model and the classic model are significant when FGM beam thickness is very small, but they are diminishing as the thickness increases.