Research on the influence of finite contact stiffness on vibration reduction of a vibro-impact nonlinear energy sink system

In this paper, the finite contact dynamics of a linear oscillator coupled with a vibro-impact (VI) nonlinear energy sink (NES) is studied, and the influence of the finite contact stiffness on the response regime and vibration reduction performance is discussed. In this way, a two-degree-of-freedom system of a linear oscillator (LO) with the attached VI-NES based on the finite contact model is built, and the novel form of VI-NES combined piecewise and impact dynamics which is named Piecewise-Impact NES (PI-NES). The response regime and vibration reduction performance caused by the change of contact stiffness for different clearances of PI-NES are discussed. It is found that the contact stiffness will affect the internal impact numbers during an excitation period of LO, which resulting in the change of VI-NES vibration reduction and the migration of the system operating state between stable and unstable states. Further, based on the response regime evolution effect, the system under the state with poor vibration reduction can be transformed to the two symmetric impacts state with obvious amplitude suppression by adjusting the contact stiffness, so that the energy transfer and dissipation efficiency can be enhanced. Finally, the optimal analysis of stiffness and PI-NES clearance parameters is carried out, and the design criteria of system parameters under different stiffness intervals are obtained. It is found that the better vibration suppression performance will be obtained on the boundary between symmetric impacts state and SMR state under different contact stiffness.