Sadakathullah Appa College (Affiliated to Manonmaniam Sundaranar University), India

This study presents a numerical investigation of primary ($V_{pri}R$), subharmonic ($V_{sub}R$), and superharmonic ($V_{super}R$) vibrational resonances in a parametric Duffing oscillator driven by an amplitude-modulated (AM) force. The excitation comprises a low-frequency component ($\omega$) and two high-frequency sidebands ($\Omega \pm \omega$). Through numerical simulations, we compare the resonant responses of the AM-forced system against a benchmark dual-frequency driven model. We delineate the parameter regions supporting steady-state oscillations and utilize amplitude-frequency curves to evaluate the influence of system parameters. The analysis reveals complex nonlinear behaviors, including jump phenomena, hysteresis, and bistability in the system's response amplitudes.