Free vibration analysis of pre/post-buckled rotating functionally graded sandwich micro-beams

This paper deals with free vibrations of pre/post-buckled rotating functionally graded sandwich micro-beams. The thermo-mechanical characteristics of functionally graded material phases are temperature dependent. The governing equations are in the framework of Euler–Bernoulli beam assumptions alongside with the von-Karman strain–displacement relation. The size effect is introduced into the equations of motion by employing the modified couple stress theory. The finite element technique is applied to the nonlinear governing equations to discretize the equations of motion. The Newton–Raphson technique is accompanied by a proposed algorithm to release the fundamental pre/post-buckling natural frequency. The significance of the material length scale parameter, the power law exponent, the rotation speed, the slenderness ratio and the rotor radius on the outcomes is examined.