Analysis of vibrational resonance in a nonlinear system with softening and hardening stiffness behaviours

Abstract This study examines vibrational resonance (VR) in a nonlinear vibratory system subjected to simultaneous weak low-frequency (LF) and strong high-frequency (HF) excitations. Analytical methods, supported by numerical simulations, are employed to examine how the interplay between stiffness parameters and HF signal properties shapes the system’s dynamic response. Results reveal that incorporating negative stiffness elements, in combination with HF forcing, significantly influences the emergence and tunability of VR states. In particular, controlled modulation of the spring constants within the double-well potential regime enables precise resonance tuning. These insights provide a foundation for designing advanced nonlinear vibration control systems capable of suppressing large-amplitude oscillations, improving energy efficiency, and enhancing vibration isolation performance.