Suppression of self-excited vibrations using tuned mass damper or nonlinear energy sink

This study investigates the vibration suppression of a self-excited system (SES) featured by limit cycle oscillation (LCO) even when there is no external harmonic loading. Such system with and without external harmonic forcing equipped with a tuned mass damper (TMD) or a nonlinear energy sink (NES) as vibration absorber is investigated. Analytical, semi-analytical harmonic balance with alternating frequency/time (HB-AFT) scheme, and Runge–Kutta (RK) based numerical integration methods are employed to obtain the dynamic response. The vibration suppression performance of the TMD and the NES is evaluated from the perspective of the displacement and vibration power flow. The dynamic response of the primary mass and the power absorption by the absorber are used as performance indices. It is shown that the nonlinear system can exhibit complex nonlinear energy flow phenomena. The optimal stiffness coefficient and damping ratio designs of the TMD for unforced SES are obtained. For the forced SES, an optimization design strategy based on the equal peak method for the TMD is proposed based on the equal-peak method. It is shown that TMD can provide good performance in vibration suppression. Optimization design of the NES is carried out, and the results show that NES could expand the range of effective suppression. In the forced system, the NES shows good robustness and nonlinear dominant energy distribution. The research findings provide valuable insights for designing high performance vibration suppression devices for self-excited systems.