Nonlinear dynamics of a functionally graded nonlocal nanobeam in thermal environment by using incremental harmonic balance and Melnikov method

Abstract

In this paper, we investigate the nonlinear dynamics of a functionally graded (FG) nanobeam with geometric nonlinearity embedded in the Kelvin-Voigt viscoelastic medium. By using the D’Alembert principle, a nonlinear partial differential equation is obtained for transverse motion of FG nanobeam subjected to external and parametric excitations and thermal load. Bifurcations and rout to chaos are investigated by using the Galerkin and incremental harmonic balance method. Criteria of existence of chaos under the influence of different types of external excitation is given based on the Melnikov method. Moreover, effects of system parameters on the periodic and chaotic motions are investigated through several numerical examples.