Nonlinear dynamic study of non-uniform microscale CNTR composite beams based on a modified couple stress theory

Abstract

This study aims at investigating the nonlinear dynamic behavior of microscale carbon nanotube reinforced (CNTR) composite Euler–Bernoulli beams with a non-uniform cross-section, based on a modified couple stress theory (MCST). The nonlinear partial differential equations (PDEs) of motion are established based on the Von-Karman nonlinear strain–displacement relationship and Hamiltonian principle. The coupled PDEs are reduced to a single PDE, by neglecting the effects of the axial inertia and considering two different types of boundary conditions (i.e. clamped–clamped and clamped–free). At the same time, the single PDE is reverted to a nonlinear ordinary differential equation (ODE) by means of the Galerkin approach, and it is solved by using a semi-inverse method and the method of multiple time scales (MTS) for a free and forced vibration analysis, respectively. A large systematic numerical analysis is here performed to check for the sensitivity of the nonlinear response of CNTR composite beams to different boundary conditions and reinforcement parameters, with useful scientific insights for further computational investigations on the topic.