Vibro-Impact NES: A Correlation Between Experimental Investigation and Analytical Description

Abstract

In this work the dynamics of a Vibro-Impact Nonlinear Energy Sink (VI-NES) is experimentally investigated via a harmonically forced single-degree-of- freedom linear oscillator (LO) to which a VI-NES is attached. Depending on external force amplitude and frequency, either a Strongly Modulated Response (SMR) or a constant amplitude response (CAR) is observed. In both cases an irreversible transfer of energy occurs from the LO towards the VI-NES: process known as passive Targeted Energy Transfer(TET). Furthermore, the problem is analytically studied by using the multiple scales method. For the fast and the slow time scales the Slow Invariant Manifold (SIM) is obtained. The 0-order SIM shows the existence of a stable and an unstable branch of solution, and of an energy threshold (a saddle-node bifurcation) for the solutions to appear. Subsequently the 1-order SIM is calculated to find the fixed points of the problem. When a stable fixed point exists, the system is naturally drawn to it and a CAR is reached. Otherwise a SMR state is established and no stable point is attained. Finally a good agreement between experimental and analytical results is shown.