Bifurcation Control of Quasi-Zero Stiffness Isolators Using Cam-Based Piecewise Damping: Parametric Optimization and Stability Analysis

To synergistically optimize the resonance peak suppression and wide-band vibration isolation capability of the quasi-zero-stiffness (QZS) vibration isolator, this paper proposes a novel QZS system incorporated with a cam-based piecewise damping (CBPD) mechanism. A nonlinear dynamic governing equation of the presented isolation system is formulated, and the averaging method is adopted to acquire the first-order approximate analytical solutions characterizing the system’s primary resonance behaviors. The Routh-Hurwitz stability criterion is employed to quantitatively delineate the stable parameter ranges for the system’s steady-state resonant responses. By conducting parametric analysis of force transmissibility and amplitude-frequency characteristics, the intrinsic mechanism of saddle-node bifurcation in the primary resonance region is revealed, and yields a targeted parametric design principle to avoid undesired dynamic jumping behaviors. Furthermore, an optimal design method for piecewise clearance based on the quasi-fixed point theory is proposed, which clarifies the functional boundaries and influence laws of the piecewise damping ratio. The results demonstrate that piecewise damping can effectively reshape the topology of the system's parameter space and generate stability windows by inducing the splitting of unstable regions, thereby efficiently suppressing nonlinear jump phenomena. Global dynamic analysis further verifies that the CBPD mechanism blocks the chaotic evolution path induced by period-doubling bifurcations and constrains multi-attractor coexistence, substantially enhancing the system’s dynamic stability. The proposed scheme effectively enhances the system robustness under large-amplitude excitation without deteriorating high-frequency isolation capacity, offering a viable technical reference for the full-band performance optimization of QZS vibration isolators.