Nonlinear forced vibrations of nonlocal strain gradient microbeams

Abstract

This paper investigates nonlinear forced vibrations of homogeneous Euler-Bernoulli microbeams with clamped-clamped boundary conditions. Here, the nonlocal strain gradient theory is incorporated to achieve the governing nonlinear partial differential equation of motion, including mid-plane stretching and damping effects. Using the Galerkin approach, a reduced equation of motion is derived under a central harmonic force. The perturbation technique is employed to examine the nonlinear forced vibration behavior of microbeam. Frequency responses of microbeam are presented for primary, super-harmonic, and sub-harmonic resonances. Simulation results indicate role of size effect on the vibration behavior of microbeam. Moreover, the effects of different physical parameters on the vibration behavior of microbeam are studied. Finally, the proposed approach is compared with a numerical solution to demonstrate the accuracy and validity of the presented analytical solution.