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.

基于修正的耦合应力和非经典的Timoshenko束理论，这里评估了受到运动粒子影响的弹性连接双纳米束系统的非线性强迫振动。假定该系统位于弹性介质上。汉密尔顿原理和伽勒金方法分别用于控制系统运动方程和相应的边界条件，并求解这些方程。数值研究表明，通过应用非线性和改进的耦合应力理论，可以预测该系统比通过线性和经典理论获得的系统更坚硬。要确定不同参数的影响，例如材料长度标度，中间层和介质的弹性刚度模量以及运动粒子的速度对系统振动的影响，进行参数研究。材料长度尺度对系统的动力响应具有重大影响，这表明经典理论无法预测纳米束系统的动力行为。中间层和介质的弹性刚度模量以及运动粒子的速度对双纳米束系统的动态挠度都有相当大的影响。