Performance and tuning of a chaotic bi-stable NES to mitigate transient vibrations

A nonlinear energy sink (NES) passively reduces transient vibration energy of a typically impact loaded mechanical system. It is locally connected to the vibrating system through a nonlinear connecting stiffness. For a NES to perform efficiently, through targeted energy transfer (TET), the vibration levels need to exceed a well-defined threshold, below which the NES performs poorly. This threshold can be lowered by considering a NES with a bi-stable connecting stiffness. A bi-stable NES (BNES) has two stable equilibria. Besides vibrating in TET regime, a BNES can also vibrate chaotically or close to one of its equilibria, called intra-well vibrations. However, during both chaotic and intra-well vibrations, the mitigating performance of the BNES is poor. Here, a novel tuning method is developed, which finds the boundary between chaotic and TET regime, such that the BNES avoids the chaos and operates with the more performant TET. This boundary is found by numerically calculating the Lyapunov exponent, a measure for chaos. To quantify performance, two algebraic expressions, requiring no simulations, are derived in the paper expressing the speed of vibration mitigation and expressing the residual vibration energy left after TET. The result is a generic tuning methodology that not only ensures the BNES operates in the efficient TET regime, but also guarantees optimal speed of vibration mitigation. The developed performances measures in function of the NES’s parameters are to the point and easy to use. The tuned BNES shows a superior robustness w.r.t detuning compared to the linear vibration absorbers.