Impact of NDF control on stability and bifurcation of a quasi-zero stiffness isolator under resonance and external excitation

Abstract This study investigates vibration suppression in quasi-zero stiffness isolators (QZSIs), which, despite their superior low-frequency isolation capability, are highly sensitive to nonlinear effects and prone to resonance amplification and chaotic oscillations that can severely degrade system performance. To address this critical limitation, a nonlinear derivative feedback (NDF) controller is proposed as a cost-effective and robust solution to enhance stability and suppress undesired vibrations. Approximate analytical solutions (AS) are derived using the multiple timescales method (MTSM) and validated against numerical solutions (NS) obtained with the fourth-order Runge–Kutta (RK-4) method. By eliminating secular terms, resonance conditions and stability regions are identified via frequency and resonance response analyses, supported by the Routh–Hurwitz stability criterion. The nonlinear dynamic behavior of the controlled system is further examined using bifurcation diagrams, Lyapunov exponent spectra (LES), Poincaré maps (PMs), and phase portraits to reveal transitions between periodic, quasi-periodic, and chaotic motions. Compared with other control strategies, the proposed NDF controller achieves superior vibration suppression efficiency of up to 99.511% while maintaining a lower implementation cost. The results confirm that NDF control significantly improves the dynamic response, stability, and chaos mitigation of QZSIs, thereby enhancing their reliability in practical applications such as aerospace, infrastructure, healthcare devices, and renewable energy systems. The novelty of this work lies in providing a comprehensive analytical and nonlinear dynamic assessment of NDF-controlled QZSIs offering new insights into resonance suppression and the long-term stability of highly sensitive isolation systems.