Stochastic Resonance and Safe Basin of Single-Walled Carbon Nanotubes with Strongly Nonlinear Stiffness under Random Magnetic Field

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.

Dynamic and instability analysis of single walled carbon nanotubes with geometrical imperfections resting on elastic medium in a magneto-thermally-electrostatic environment with impact of Casimir force using homotopy perturbation method

“…The obtained results was compared with fourth order Runge-Kuta numerical solutions and there are in accuracy agreement as the new obtain results can be use as benched mark for future investigations. Xu et al (2018) developed nonlinear model of single-walled carbon nanotube (SWCNTs) and study nonlinear dynamical characteristic of such single-walled carbon nanotubes which is subjected to random magnetic fields permeability/strength. Furthermore, Eringen's differential constitutive model considered effects of non-local microstructure and energy function method (EFM) is used to obtained the nonlinear dynamical response like natural frequency.…”

System Dynamics Modelling and Simulation of Computer Control Systems for Steel Ingot Furnaces

“…Perceived delays also involve stock, even though the stock is not a material flow. It is important to see what is coming in and what is going out of an organisation so that the results of production can be fast-tracked [34]. The stock depends on the inflow and outflow of material; for the stock to be in equilibrium, the total inflow of material must be equal to the total outflow of material.…”

“…Different decisions affect the stock's state of equilibrium. As the stock changes, information about the buffers will influence the inflows and outflows of the stock, and the feedback loops will operate to restore the balance of the stock [34].…”