Steady-state forced vibrations of magneto-electro-elastic Timoshenko nanobeams

This paper aims to investigate forced vibrations of Timoshenko nanobeam, which is under axially loaded. The material is assumed to be magneto-electro-elastic coupling and surface effect is considered. The governing equations and the corresponding boundary conditions are derived, with the Hamilton principle. For steady-state forced vibrations, the variable separation and the Laplace transform methods are employed to obtain the Green’s function, for three typical kinds of beams, namely Hinged-Hinged, Clamped-Clamped, and Clamped-Free. Numerical examples are performed to check the validity of the present solutions and to evaluate the influence of magneto-electric coupling and surface effect on the forced vibration of the beams.