Design of a piecewise-stiffening Nonlinear Energy Sink for torsional vibration attenuation

Abstract

Torsional vibrations are undesirable in rotating machinery, and demands for better performance and material savings to reduce weight exacerbate this issue by triggering resonance conditions. The Nonlinear Energy Sink (NES) offers a robust and effective vibration attenuation solution. In this research, a 2 Degree-Of-Freedom torsionally vibrating host structure is equipped with a NES having piecewise-linear stiffness approximating a cubic nonlinearity. The first-order Complexification-Averaging (CxA) method is used to analyse the Slow Flow dynamics on the response envelope, and a NES tuning methodology based on the Slow Invariant Manifold is proposed for 1:1 resonance attenuation for two resonance frequencies of the host system. The mechanical design of the NES is optimised for minimal stresses and fatigue while avoiding local resonances of the individual components. Experiments and numerical simulations validate the CxA method, and indicate the presence of Strongly Modulated Response regime and an Isolated Resonance Curve in the vicinity of resonance. Significant resonant response attenuation is achieved for both the first mode ($>80\text{\%}$) and the second mode ($>65\text{\%}$) over a wide range of forcing amplitudes, with possibility of further improvements. In this regard, design modifications that allow for effective multi-modal attenuation are presented. As such, a complete toolchain has been developed to obtain an NES design which can be applied to a wide range of torsional vibration applications.