Probability-of-existence of vibro-impact regimes in a nonlinear vibration energy harvester

• Published in: Smart materials and structures 2013-09, Vol.22 (9), p.094025-1-9
• Main Authors: Vandewater, L A, Moss, S D
• Format: Article
• Language: English
• Subjects: Bandwidth; Duffing oscillators; Energy harvesting; Exact sciences and technology; Excitation; General equipment and techniques; Harvesters; Instruments, apparatus, components and techniques common to several branches of physics and astronomy; Mathematical models; Nonlinearity; Physics; Softening; Transducers; Vibration
• ISSN: 0964-1726; 1361-665X
• DOI: 10.1088/0964-1726/22/9/094025

This paper reports on the characterization of high-energy vibro-impacting regimes in a vibration energy harvester with softening Duffing nonlinearity, by mathematical modelling and numerical analysis with experimental validation. The harvester is implemented as a base excited permanent-magnet/ball-bearing arrangement, where oscillations by the ball-bearing induce a change in magnetic flux in a wire coil, which in turn generates a voltage. Symmetric rigid aluminum stops in the harvester structure restrain the amplitude of the ball-bearing motion (within gap Δ) and thus produce vibro-impact behaviour under certain operating conditions-leading to wideband operation. These operating conditions are analysed by means of an event-driven equation switching algorithm, implementing a base-driven Duffing oscillator with conditional hyster-Hertz impact mechanics. In considering the 'probability-of-existence' of impact regimes, predictions about the frequency bandwidth of the high-energy impact state are made and compared to the experimental prototype. A trade-off between operating bandwidth and output power is noted. For the non-optimized harvester arrangement examined in this paper, with a gap Δ = 14.7 mm the bandwidth was predicted to be ∼1.3 Hz, and was measured at 0.7 Hz with an output power of 7.4 mW rms. With a gap size Δ = 2.9 mm the bandwidth was predicted to be ∼7.2 Hz, and was measured at 6.1 Hz with an output power of 54 μW rms. The authors believe that the probability-of-existence approach may be useful for characterizing the conditions required for exciting high-energy states of other nonlinear vibration energy harvesting systems.