Resonance capture cascading of non-smooth NES to mitigate multi-modal torsional vibration of MDOF rotor system

The nonlinear energy sink (NES) is capable of suppressing the multi-modal transient vibration of a multi-degree-of-freedom (MDOF) main system by means of resonance capture cascading (RCC). The principle of its vibration damping is targeted energy transfer (TET). The MDOF rotor system frequently experiences multi-modal transient torsional vibration during operation, which makes a small number of vibration absorbers urgently necessary. Consequently, in this paper, a non-smooth NES (NSNES), which possesses broadband-frequency vibration attenuation ability, is investigated for mitigating the multi-modal vibration of the MDOF rotor system. In the process of vibration suppression, RCC takes place between the MDOF rotor system and NSNES. First of all, the MDOF rotor system is transformed into a positive definite system. After adding the NSNES, modal equivalence is provided. Additionally, the slow invariant manifold (SIM) of the equivalent system is derived. Subsequently, the tuning rules and performance metrics of NSNES for the equivalent system with single-modal TET are established. By using modal decomposition, the tuning rules and performance metrics for NSNES in the MDOF rotor system for suppressing multi-modal vibration are established. Finally, the RCC phenomenon in the MDOF rotor-NSNES system in multi-modal vibration is analyzed. The influences of modal damping of the rotor system on pumping time and cascading time are examined.