1/2 and 1/3 Subharmonic Resonance Behaviors of a Rotating FG-CNTRC Beam with Geometric Imperfections

Abstract

This paper aims at investigating 1/2 and 1/3 subharmonic resonances of a rotating functionally graded carbon nanotube-reinforced composite (FG-CNTRC) beam in the presence of geometric imperfections. A general function is introduced to denote three types of imperfections containing sine, global, and local modes. At first, based on the von-Kármán geometric nonlinearity assumption, the forced vibration equation is set up. Then, the Galerkin method and multiple scale method are utilized to study subharmonic resonance behaviors. Finally, coupled effects of FG-CNTRCs, rotating motion, and geometric imperfections on subharmonic resonance responses are investigated. It is found that a specific range of the excitation amplitude and frequency motivates the subharmonic resonance behavior. The coupling of geometric imperfections and geometric nonlinearities generates the 1/2 resonance phenomena, and geometric nonlinearities result in the 1/3 resonance behavior. Both the imperfection mode and amplitude can affect the resonance response and resonance regions. Moreover, in contrast with the 1/3 subharmonic resonance, geometric imperfections produce greater influence on the 1/2 subharmonic resonance.