Nonlinear Resonance Dynamics of SWBNNTs in Viscoelastic Media: Primary, Subharmonic, and Superharmonic Regimes

This study investigates the nonlinear vibrational behavior of single-walled boron nitride nanotubes (SWBNNTs) using a nonlinear Euler-Bernoulli beam model. The governing partial differential equations are reduced to a set of ordinary differential equations through Galerkin's method employing trigonometric shape functions. The multiple time scales method is then applied to analyze the nonlinear frequency response under primary, subharmonic, and superharmonic resonances, and implicit analytical expressions for the frequency response are derived. A comprehensive parametric study is conducted to examine the influences of stiffness, excitation amplitude, damping coefficient, and detuning parameter on the nonlinear dynamic behavior. The results reveal that increased stiffness significantly suppresses nonlinear effects by enhancing resistance to deformation, while higher excitation amplitudes amplify nonlinear response intensity across all resonance cases. Subharmonic resonance exhibits response trends distinct from those of primary and superharmonic resonances, although their overall effectiveness remains comparable. Backbone curve curvature effectively captures the growth or decay of nonlinear intensity due to parameter variations. Furthermore, damping is shown to attenuate nonlinear effects owing to energy dissipation, whereas increased detuning leads to stronger nonlinear responses characterized by pronounced multi-valued behavior. These findings provide valuable insights into controlling and tuning the nonlinear vibration characteristics of SWBNNT-based nanostructures.