Design and experimental study of a Nonlinear Energy Sink coupled to an electromagnetic energy harvester

Abstract

Nonlinear vibration absorbers, commonly referred to as Nonlinear Energy Sinks (NESs), have been the object of several theoretical and experimental studies over the past decade. This work illustrates the theoretical design and experimental realization of a Nonlinear Energy Sink coupled to an energy harvester. The mass of the Magnetic-Strung NES is a magnet which is linked to the primary system by means of two strings with adjustable pretension that work transversally. The restoring elastic force of the strings is modulated by the magnetic force applied by two magnets suitably located on the primary mass. Either a cubic or a bistable configuration may be obtained, depending on the distance of the additional magnets, NES's efficiency as an absorber is studied on a harmonically forced single degree-of-freedom primary system. The Target Energy Transfer (TET) from the primary system to the NES, as well as different response regimes like the Strongly Modulated Response (SMR), are experimentally observed. Furthermore, the harvesting of energy from the NES vibrations is also investigated by coupling the mechanical system with a coil for electromagnetic energy conversion. Consequently, the vibration energy of the primary mass is absorbed by the NES and finally converted into electric energy.

Introduction

A Nonlinear Energy Sink is a passive vibration absorber which is nonlinearly coupled to a primary system. The use of a Nonlinear Energy Sink (NES) as a vibration absorber has been subject of interest over the last decade with studies that have shown, in comparison to the classical linear Tuned Mass Damper (TMD), that the NES could be effective over a broader frequency range and only require a small additional mass. It has been shown that the nonlinear attachments can lead to an irreversible energy transfer from the primary system towards the NES, this process is known as Targeted Energy Transfer (TET) or pumping [[1], [2], [3], [4], [5]]. Experimental works [[6], [7], [8]] have shown that the dynamics which govern this energy transfer phenomenon can be defined as a 1:1 resonance capture between the primary mass and the NES. One important and intriguing feature of a NES system is its ability to tune itself to the primary system response, since the NES does not have its own natural frequency due to its intrinsic nonlinear nature. TET under external forcing has been investigated both theoretically [9] and experimentally [10]; these studies have shown that NES systems can exhibit multiple responses of interest including steady state constant amplitude regimes and Strongly Modulated Responses (SMR). NESs have also been studied to passively control instabilities. For example, in Ref. [11] a NES is used to control the limit cycle behavior of a Van der Pol oscillator. In Refs. [[12], [13], [14], [15]] it was used to suppress aeroelastic instabilities. Most of the aforementioned works considered a nonlinearity with a cubic stiffness term. Fundamentally, the basic principle was to use a geometric nonlinearity of an elastic element to obtain a cubic nonlinearity in the restoring force. Nevertheless, the nature of the nonlinearity used in the NES may be of any kind. Later studies have explored other ideas such as: non-polynomial functions [16], multiple states of equilibrium [17], non-smooth functions and Vibro-Impacts [[18], [19], [20], [21], [22]].

Energy harvesting from the environment [23] has recently received considerable attention and many works have been motivated by advancements in the microelectronics industry, which have enabled a reduction in the power consumed by MEMS devices [24,25]. Solar, chemical, and thermal methods have been extensively investigated and recognized as potential sources of energy. The harvesting of energy from either structural born vibrations or the motions of rigid structures has also shown much promise. Many early works considered inertial generators with linear behavior [26]. A primary limitation of linear inertial generators is their narrow-band efficacy; i.e. their performance significantly decreases for any mismatch of the excitation and resonance frequency [27]. Tuning the device's resonance and widening the bandwidth by adding many oscillators are some methods that have been studied to overcome this limitation in Refs. [28,29].

Analogous to the vibration absorber, nonlinearity seems to also offer the potential to improve performance in energy harvesting systems. One of the first experimental investigations of an energy harvester specifically designed to exhibit a nonlinear response was described in Ref. [30] where magnetic levitation was used to extend the device bandwidth. A similar study based on piezoelectric energy conversion is presented in Ref. [31]. A piezoelectric nonlinear energy harvester is presented in Ref. [32] where high power output and wide working bandwidth are reached. The same authors have also investigated a new magnetoelectric generator in Ref. [33]. Many systems demonstrate the advantages of monostable Duffing oscillators for increased bandwidth. The bistable Duffing oscillator has also been investigated for energy harvesting in Refs. [34,35].

In this paper the two research fields of nonlinear vibration absorbers and energy harvesting are combined. The study of a new concept of cubic NES coupled to an electromagnetic harvester is presented. By means of a magnetic force, the nonlinear force between the NES and the primary system can be adjusted and shaped to test different configurations. Three configuration are experimentally tested and the results are compared to highlight the potential use of the device as an absorber and/or energy harvester.