Research on Target Energy Transfer and Energy Dissipation of Coupled Fractional-Order Inerter-Based Nonlinear Energy Sinks Vibration System

This study investigates the critical role of resonance capture dynamics in determining the energy dissipation performance of nonlinear energy sinks (NES). A fluid inerter combining mass amplification and damping characteristics is proposed as a core component, based on which two configurations of fractional-order NES (configured in series and parallel) are systematically constructed. The applicability of the complex averaging method in fractional-order systems has been addressed through fractional calculus (such as Leibniz properties), enabling it to be analyzed like integer-order systems. Employing the multi-scale perturbation method, the energy transfer mechanism between the primary oscillator and the NES is derived, leading to the analytical determination of optimal cubic stiffness and maximum energy transfer efficiency. Comparative simulation shows that the parameters of the inerter directly affect the magnitude of critical damping. The optimal cubic stiffness design method is more reliable than traditional methods and can ensure effective target energy transfer triggering. Further analysis of dissipation time shows that the performance of fractional-order NES is superior to integer-order NES; notably, the dissipation time of series fractional-order NES is significantly shorter than that of parallel and traditional NES. In summary, this study provides theoretical guidance for the design of lightweight and high-performance NES and will also promote the application of fractional calculus theory in the field of engineering vibration reduction.