On optimal performance of nonlinear energy sinks in multiple-degree-of-freedom systems

TL;DR

This paper investigates how nonlinear energy sinks can be optimally tuned to maximize energy transfer in multi-degree-of-freedom systems, revealing robustness advantages over linear systems and emphasizing the role of homoclinic orbits.

Contribution

It develops a perturbation-based framework for optimizing nonlinear energy sinks in multi-degree-of-freedom systems and compares their performance to linear counterparts.

Findings

Nonlinear energy sinks effectively transfer energy for impulsive excitations.

Optimal parameters are derived analytically for given impulsive inputs.

Nonlinear energy sinks show greater robustness to parametric perturbations.

Abstract

We study the problem of optimizing the performance of a nonlinear spring-mass-damper attached to a class of multiple-degree-of-freedom systems. We aim to maximize the rate of one-way energy transfer from primary system to the attachment, and focus on impulsive excitation of a two-degree-of-freedom primary system with an essentially nonlinear attachment. The nonlinear attachment is shown to be able to perform as a `nonlinear energy sink' (NES) by taking away energy from the primary system irreversibly for some types of impulsive excitations. Using perturbation analysis and exploiting separation of time scales, we perform dimensionality reduction of this strongly nonlinear system. Our analysis shows that efficient energy transfer to nonlinear attachment in this system occurs for initial conditions close to homoclinic orbit of the slow time-scale undamped system, a phenomenon that has been previously observed for the case of single-degree-of-freedom primary systems. Analytical formulae for optimal parameters for given impulsive excitation input are derived. Generalization of this framework to systems with arbitrary number of degrees-of-freedom of the primary system is also discussed. The performance of both linear and nonlinear optimally tuned attachments is compared. While NES performance is sensitive to magnitude of the initial impulse, our results show that NES performance is more robust than linear tuned-mass-damper to several parametric perturbations. Hence, our work provides evidence that homoclinic orbits of the underlying Hamiltonian system play a crucial role in efficient nonlinear energy transfers, even in high dimensional systems, and gives new insight into robustness of systems with essential nonlinearity.