Dynamic characteristics of a series-parallel-II inertial nonlinear energy sink for vibration control - Wu, Ziying; Zhu, Rongxian; Wang, Yuanzhi; Guo, Xi; Yan, Jiyu; Wang, Zizheng (Sound & Vibration, 2026)
This paper proposes a novel series-parallel-II inertial nonlinear energy sink (SPII-I-NES) integrated with Coulomb friction. The governing equations of motion are formulated for the primary system coupled with the SPII-I-NES under both harmonic excitation and Gaussian white noise. By combining the harmonic balance method with the arc-length continuation method (ALM), quasi-analytical amplitude response solutions are derived for the primary structure and the SPII-I-NES under harmonic excitation. Numerical simulations demonstrate that the SPII-I-NES exhibits significantly superior vibration-suppression performance compared to the NES and linear series-parallel-II inerter configurations. Furthermore, the equivalent additional mass introduced by the SPII-I-NES is smaller than that of both the NES and the linear series-parallel-II inerter. The influence of key parameters on the dynamic responses of the primary system and SPII-I-NES is systematically investigated, including nonlinear stiffness coefficients, nonlinear damping ratios, and friction force. Results indicate that, compared to nonlinear damping ratios and friction forces, the nonlinear stiffness coefficients of the SPII-I-NES play a more dominant role in inducing strong nonlinear behaviors in both systems. Notably, when nonlinear Coulomb friction is considered, the primary system may exhibit quasi-periodic or chaotic vibration patterns. Under Gaussian white noise excitation, stochastic jumps or bifurcations are observed in both the primary system and the SPII-I-NES, highlighting the complex dynamic interactions introduced by this configuration.