Nonlinear dynamics and chaotic behavior of curved self-sustaining BNNTs under combined thermal and magnetic fields

This study examines the primary resonance and chaotic vibration behavior of a curved single-walled boron nitride nanotube (CSWBNNT) subjected to axial thermo-magnetic loading and transverse harmonic excitation on a viscoelastic foundation. The system is modeled using nonlocal Euler–Bernoulli beam theory and reduced to an ordinary differential equation via a single-mode Galerkin approximation. The method of multiple scales is applied to derive analytical expressions for the primary resonance response of a clamped–clamped CSWBNNT. Parametric effects, including nonlinear contributions of the viscoelastic medium, sinusoidal curvature amplitudes, and Young’s modulus value, are investigated with emphasis on frequency response, jumping phenomena, and instability regions. Numerical simulations using the Runge–Kutta method generate bifurcation diagrams, phase plane trajectories, and Poincaré maps to characterize periodic and chaotic dynamics. Results reveal that thermo-magnetic forces strongly influence resonance behavior, while chaotic vibrations are highly sensitive to excitation amplitude, underscoring the complex interplay between external loading and nonlinear structural parameters.