The simultaneous effect of small-scale coefficient and bandwidth on the noise-induced chaos of single-walled carbon nanotubes under broadband axial magnetic fields

Abstract

This article investigates the dynamic stability and the boundaries of chaotic zones in the response of a single-walled carbon nanotube (SWCNT) subjected to an axial stochastic non-Gaussian magnetic field using a nonlocal elasticity approach. First, the nonlinear equations governing the random vibration of the system are derived by introducing several dimensionless parameters. Second, a modified version of Melnikov’s function for random systems is developed, which leads to an analytical expression for determining the boundaries of the chaotic zone. The boundaries of this chaos zone are plotted and discussed in terms of the small-scale coefficient (SSC), the mean value of the magnetic field intensity (MFI), and the bandwidth of the noise. The proposed method is versatile, applicable to a wide range of excitations, including almost harmonic, wideband, narrowband, and nearly white-noise excitations. The findings provide valuable insights into how the aforementioned dimensionless parameters influence system instability, serving as a foundation for the design of such systems.