High-dimensional parametric bifurcation analysis of a novel series QZS-TMD for broadband stable vibration attenuation

This study develops a novel series-connected quasi-zero-stiffness tuned mass damper (QZS-TMD) to overcome the inherent limitations of conventional linear TMDs and QZS vibration absorbers, including their narrow effective attenuation bandwidths and the inability to synchronously regulate resonant and anti-resonant oscillation peaks. Focusing on the high-dimensional coupled weakly nonlinear dynamics of the proposed 3-DOF series QZS-TMD system, this paper establishes analytical criteria for the coexistence of saddle-node and Hopf bifurcations and systematically maps their global boundaries. Furthermore, the global evolutionary routes from periodic steady states to chaotic responses are quantitatively identified. An equal-peak parametric optimization scheme is developed to simultaneously attenuate resonant and anti-resonant amplitudes while suppressing chaotic multistability and jump resonances. The optimized parameters ensure stable periodic motions across the entire excitation frequency range. Quantitative power flow analysis demonstrates that the geometric nonlinearity of the series QZS layout dominates energy dissipation, absorbing more than 90% of the input vibrational energy within the anti-resonance band. The analytical bifurcation criteria established in this work provide robust theoretical foundations for the parametric design of high-dimensional coupled vibration absorption systems.