Nano-resonator dynamic behavior based on nonlocal elasticity theory

Abstract

By decreasing the thickness of micro- and nano-beams, classical continuum theory is not accurate to model the static and dynamic response of them due to absence of length scale parameter. In this paper, nonlocal elasticity theory is used to detect the chaos in nano-resonator. First mode shape of nano-beam is found and Galerkin method is used to convert the governing partial differential equation to an ordinary differential equation. Melnikov method is used to determine the critical value of AC actuation voltage resulting chaotic motion. Effects of nonlocal parameter and beam thickness on stability region of resonator are investigated and it is shown that increasing the nonlocal parameter and decreasing the beam thickness increases the difference between stability regions obtained by two theories.