NONLINEAR OSCILLATION ANALYSIS OF NANOBEAMS UNDER SOFT EXCITATION INCLUDING SURFACE FREE ENERGY EFFECTS

The main incentive of this study is to analyze primary resonance of nanobeams in presence of surface free energy effects. Considering geometrical nonlinearities based onvon Karman relation. a refined Euler-Bernoulli beam model is developed through Gurtin-Murdoch elasticity theory in which surface stress effects are incorporated. Nonlinearities are assumed to be small and the external force is in the order of nonlinearities to study solely soft excitation and primary resonances. Governing sixe-dependent differential equation of motion is obtained by using a variational approach based on Hamilton s principle. By using Galerkin procedure, the nonlinear partial differential equation is convened to a nonlinear ordinary differential equation. Method of intiltiple scales is utilized to obtain an approximate closed form solution.Parametric analysis is carried out to study influence of surface moduli on frequency-response and amplitude- response curves. It is observed that surface effects are critical and ignoring them will cause large errors in nonlinear analysis. Albeit significant at nanoscalc, it is indicated that surface effects diminish rapidly at larger scales.

Keywords:

Nanomechanics. Nonlinear oscillation , Size dependency , Method of multiple scales. Duffing equation