Linear and nonlinear vibrations of strain gradient beams with rough surface

Abstract

This paper aims to study the effect of surface roughness on the linear and nonlinear free vibration behaviors of microbeams based on the strain gradient theory. Linear and nonlinear equations of motion and boundary conditions are derived by using the Hamilton’s principle. A closed-form solution of strain gradient beams (SGBs) is obtained by solving a general sixth-order differential equation. Furthermore, by utilizing the linear mode and Galerkin’s method, an exact solution for nonlinear vibration is also obtained for SGBs. A detailed parametric study is performed to study the influences of surface roughness, scale parameter, beam thickness, and boundary condition on the linear and nonlinear vibration behaviors of SGBs. The present study may provide help for optimal designing and fabricating micro-/nano-resonators.