Abstract
In this paper, a kind of single-walled carbon nanotube nonlinear model is developed and the strongly nonlinear dynamic characteristics of such carbon nanotubes subjected to random magnetic field are studied. The nonlocal effect of the microstructure is considered based on Eringen’s differential constitutive model. The natural frequency of the strongly nonlinear dynamic system is obtained by the energy function method, the drift coefficient and the diffusion coefficient are verified. The stationary probability density function of the system dynamic response is given and the fractal boundary of the safe basin is provided. Theoretical analysis and numerical simulation show that stochastic resonance occurs when varying the random magnetic field intensity. The boundary of safe basin has fractal characteristics and the area of safe basin decreases when the intensity of the magnetic field permeability increases.
Highlights
With the advancement of the nanotechnology, carbon nanotubes (CNTs) have been among the most promising components in nanoelectromechanical systems (NEMS)
Theoretical analysis and numerical simulations show that stochastic resonance occurs when varying the random magnetic field intensity
It is concluded that the boundary of safe basin has fractal characteristics and the area of safe basin decreases when the intensity of the magnetic field permeability increases
Summary
With the advancement of the nanotechnology, carbon nanotubes (CNTs) have been among the most promising components in nanoelectromechanical systems (NEMS). CNTs have attracted worldwide attention because of their potential applications in many areas of science and engineering such as electronics, chemistry, nanoengineering, materials science, thermal and other physical attributions [1–3] They have been widely used in NEMS, for example in nanobiological devices. In order to obtain a good understanding of CNTs and to design new nanodevices, it is very important to build more accurate theoretical models and to analyze their properties For these nanostructures at such minute scales, the classical (local) continuum mechanics models are deemed to fail because the classical models disregard surface and size effects and assume the stress state at a given point to depend uniquely on the strain state at that identical point.
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