Nonlinear vibration of an elastically connected double Timoshenko nanobeam system carrying a moving particle based on mo
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O R I G I NA L
Shahram Hadian Jazi
Nonlinear vibration of an elastically connected double Timoshenko nanobeam system carrying a moving particle based on modified couple stress theory
Received: 12 December 2019 / Accepted: 3 August 2020 © Springer-Verlag GmbH Germany, part of Springer Nature 2020
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. Keywords Nanobeam · Double-beam system · Modified couple stress theory · Non-classical Timoshenko beam theory · Moving load
1 Introduction Due to its useful mechanical properties, nanobeam system is one of the widely applied nanostructures in MEMS- and NEMS-like sensors, oscillators, switches, and actuators [1–3]. Consequently, the focus of many studies is on analyzing the dynamical behavior of these systems. Size dependency is one of the major phenomena in micro-/nanostructures, which affects the mechanical behavior of these systems [4,5]. Experimental tests show that the material characteristics like Young’s modulus, bending rigidity, etc., increase by decreasing the size in micro- and nanoscales. In [4], it has been shown that by decreasing the diameter of copper wire from 170 to 12 μm, its torsional hardening increases by a factor of 3. By performing experimental bending tests, Stolken and Evans [6], Shrotriya et al. [7], and Haque and Saif [8] showed that by an increase in the beam thickness, a great decrease occurs in the bending strength of ultra-thin beams. The size dependency of the mechanical properties has also been observed in [9–11] by applying experimental tests. The above experimental researches imply that for micro-/nanoelements whose characteristic sizes like thickness and diameter are in the order of specific amounts, the material properties and consequently the behavior are highly dependent on their dimensions. These specific amounts which represent the size d
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