Bending and vibration of functionally graded microbeams using a new higher order beam theory and the modified couple stress theory

Static bending and free vibration of functionally graded (FG) microbeams are examined in this paper based on the modified couple stress theory (MCST) and various higher order beam theories (HOBTs). This non-classical microbeam model incorporates the material length scale parameter which can capture the size effect. The material properties of the FG microbeams are assumed to vary in the thickness direction and are estimated through the Mori–Tanaka homogenization technique. The governing equations and the related boundary conditions are derived using Hamilton’s principle. The Navier-type solution is developed for simply-supported boundary conditions. Numerical results are presented to investigate the influences the material length scale parameter, different material compositions, and shear deformation on the bending and free vibration behavior of FG microbeams. Some of the present results are compared with the previously published results to establish the validity of the present formulation. It is established that the present FG microbeams exhibit significant size-dependence when the thickness of the microbeam approaches to the material length scale parameter.