The evaluation of a nonlinear energy sink absorber based on the transmissibility

A generalized transmissibility is proposed to evaluate nonlinear vibration absorbers. Due to possible existence of higher order harmonics and aperiodic motion, the root mean square is employed to define the transmissibility. The transmissibility beyond harmonic motion is applied to measure vibration reduction of a structure coupled with a nonlinear energy sink. Periodic steady-state responses of the coupled system are analytically predicted by the method of harmonic balance, and the stabilities of the responses are determined. The effects of parameters of the nonlinear energy sink on the transmissibility are explored based on harmonic balance solutions and numerical simulations. Phase portraits, Poincaré map and frequency spectrum reveal that quasi-periodic motions occur when periodic responses are unstable. Finally, two evaluation approaches based on the energetics and the transmissibility are compared. The investigation demonstrates the quasi-periodic motion is an indication of the optimal transmissibility. The performance of nonlinear energy sink absorbers may be extremely sensitive to parameter variations.