A Comparison of Nonlinear Bending and Vibration of Hybrid Metal/CNTRC Laminated Beams with Positive and Negative Poisson’s Ratios

Abstract

Carbon nanotube reinforced composite (CNTRC) is one of the novel classes of advanced composite materials. This paper investigates the nonlinear bending and nonlinear vibration responses of hybrid laminated beams made of CNTRC layers bonded with metal layers on the top and bottom surfaces. We proposed a hybrid metal/CNTRC laminated beam for which out-of-plane Poisson’s ratio is negative. The effective material properties of CNTRC layers are graded in a piece-wise pattern across the thickness of the beam. The material properties of both CNTRC layer and metal layer are temperature dependent. The beams are rested on an elastic foundation and are located in thermal environments. Reddy’s higher-order beam model is used to establish the motion equations of the hybrid metal/CNTRC laminated beam. The motion equations include the von Kármán geometric nonlinearity, the thermal effects and the beam-foundation interaction. By employing a two-step perturbation approach, the bending and nonlinear vibration solutions are obtained. A comparison of nonlinear responses of hybrid metal/CNTRCl laminated beams with positive and negative Poisson’s ratios (NPRs) under different thermal environmental conditions is carried out and discussed in detail.