Thermal effect on size dependent behavior of functionally graded microbeams based on modified couple stress theory

Abstract

Thermal effect on buckling and free vibration behavior of functionally graded (FG) microbeams based on modified couple stress theory is presented. Classical and first order shear deformation beam theories are adopted to count for the effect of shear deformations. Hamilton’s principle is applied to give the governing equations, boundary and initial conditions of the FG microbeam. Using generalized differential quadrature (GDQ) method buckling load and natural frequency of FG microbeam with different boundary conditions are obtained. Some numerical results are presented to investigate effects of different parameters including temperature changes, material length scale parameter, beam thickness, Poisson’s ratio and power index of material distribution on the FG microbeam behavior. Numerical results show that modified couple stress theory predicts higher values of buckling load and natural frequency for FG microbeams. In addition, it is observed that higher temperature changes signify size dependency of FG microbeam. It is shown that Poisson’s effect on buckling load and natural frequency predicted by the current model differs significantly from classical one. Study of power index of material distribution proved that the behavior of FG microbeams differ considerably from homogeneous isotropic ones.