Chaos prediction in nano-resonators based on nonlocal elasticity theory

Abstract

By decreasing the thickness of micro- and nano- beams, classical continuum theory is not accurate to predict the static and dynamic response due to the absence of length scale parameter. In this paper, nonlocal elasticity theory is used to detect chaos in nano-resonators. In this way, first mode shape of the 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 the stability region of the resonator are investigated. It will be shown that increasing the nonlocal parameter and decreasing the beam thickness increases the difference between stability regions obtained by classical and nonlocal theories. Moreover, increasing the nonlocal parameter decreases the nonlinear stiffness and increases the critical actuation voltage which may lead to chaotic motion.