A comparative study on the torsional vibration suppression of rotor system using variable steady state nonlinear energy sink

Current studies have shown that the introduction of bistable nonlinear energy sink (B-NES) and tristable nonlinear energy sink (T-NES) can reduce the effective threshold and alleviate the separation resonance curve compared with traditional NES under the low and higher external excitation respectively. However, there is a lack of comparative studies on the performance of B-NES, T-NES and monostable nonlinear energy sink (M-NES) in the field of torsional vibration engineering application. Aimed at this limitation, a variable steady state nonlinear energy sink (V-NES) is proposed to suppress the torsional vibration of shafting. Negative stiffness is generated by the pre-compression of the spring. The proposed V-NES can be easily switched between monostable, bistable and tristable cases by the moving position of the spring bases. Based on this, the governing equation of torsional vibration coupled with V-NES after proper orthogonal decomposition (POD) reduction is derived. The approximate analytical solution of the coupled system is obtained by using complex averaging method and verified numerically. Then, the vibration reduction effects of M-NES, B-NES and T-NES on the torsional vibration of shafting are compared. Throughout the study, the motion states of strongly modulated response (SMR), interwell oscillation, and chaotic strongly modulated response (CSMR) are observed in the V-NES. Excessively high external excitation amplitudes can make V-NES exhibit CSMR, diminishing the effectiveness of vibration reduction in comparison to inter-well oscillations.