A compact analytical method for vibration of micro-sized beams with different boundary conditions

Abstract

In this article, a compact analytical method for vibration analysis of gradient elastic beams is presented to solve any combination of boundary conditions. The general frequency determinant for microbeams with general restraints are derived by using Stokes' transformation. The main advantage of this determinant is capability of considering any possible combination of boundary conditions. By assigning proper values to spring parameters in the general frequency determinant, the solutions can also be determined for the rigid boundary conditions. Numerical results are presented to investigate the influences the material length scale parameter, rotational, and translational springs on the free vibration behavior of microbeams. Some of the present results are compared with the previously published results to establish the validity of the present formulation. The microbeams with restrained boundary conditions exhibit significant size dependence when the length of the microbeam approaches to the material length scale parameter.