Nonlinear vibration of an elastically connected double Timoshenko nanobeam system carrying a moving particle based on modified couple stress theory

Abstract

Based on the modified couple stress and non-classical Timoshenko beam theories, the nonlinear forced vibration of an elastically connected double nanobeam system subjected to a moving particle is assessed here. This system is assumed to be resting on an elastic medium. Hamilton’s principle and the Galerkin method are applied to govern the equations of system motion and corresponding boundary conditions and to solve these equations, respectively. The numerical study reveals that by applying the nonlinear and modified couple stress theories the system is predicted stiffer than what is obtained through linear and classical theories. To determine the effects of different parameters like the material length scale, the elastic stiffness modulus of the interlayer and medium, and the velocity of the moving particle on the system’s vibration, a parametric study is performed. The material length scale has a significant effect on the dynamic response of the system, indicating that the classical theory cannot predict the dynamic behavior of nanosize beam systems. The elastic stiffness modulus of both the interlayer and medium and the velocity of the moving particle have considerable effects on the dynamic deflections of the double nanobeam system.