Singularity analysis on vibration reduction of a nonlinear energy sink system

Nonlinear energy sink (NES) can be used to reduce the forced vibration of the primary system. Many different kinds of periodic responses of the linear system coupled with NES have been presented in the literature. In order to reveal all kinds of periodic responses of the NES system on given parameter planes, this study intends to achieve the classification of different kinds of periodic responses of linear oscillator coupled with a NES under harmonic excitation, which is modeled as a 2-degree-of-freedom system. The amplitudes of periodic responses of the nonlinear system are obtained by using the harmonic balance method. Then a general method based on the singularity theory is proposed to reveal all kinds of periodic responses under a given set of parameters. The periodic responses include 10 kinds known responses and 4 kinds of newly-revealed responses. The complete classification of the responses ensure the reliability and the efficiency of a NES.