A Nonlinear Approach for Dynamic Responses of a Nano-beam based on a Strain Gradient Nonlocal Theory

摘要

The transverse nonlinear vibration of a nano-beam fully clamped at both two ends was investigated using a strain gradient type of nonlocal continuum theory. The small scale effect was considered to the mechanical model at nanoscale. The axial elongation of the nano-beam was taken into account and the nonlinear partial differential equation governing the transverse motion was derived. Subsequently, a perturbation method was applied to the nonlinear governing equation. The dynamical responses of the nano-beam such as transverse displacement and resonant angular frequency were obtained and they were compared with those by a numerical method. The comparison indicated the validity of the present nonlinear model and the multiple-scales analysis method.