This paper investigates the design and analysis of a novel energy harvesting device that uses magnetic levitation to produce an oscillator with a tunable resonance. The governing equations for the mechanical and electrical domains are derived to show the designed system reduces to the form of a Duffing oscillator under both static and dynamic loads. Thus, nonlinear analyses are required to investigate the energy harvesting potential of this prototypical nonlinear system. Theoretical investigations are followed by a series of experimental tests that validate the response predictions.The motivating hypothesis for the current work was that nonlinear phenomenon could be exploited to improve the effectiveness of energy harvesting devices.

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We model and experimentally validate a nonlinear energy harvester capable of bidirectional hysteresis. In particular, both hardening and softening response within the quadratic potential field of a power generating piezoelectric beam (with a permanent magnet end mass) is invoked by tuning nonlinear magnetic interactions. Not only is this technique shown to increase the bandwidth of the device but experimental results additionally verify the capability to outperform linear resonance. Engaging this nonlinear phenomenon is ideally suited to efficiently harvest energy from ambient excitations with slowly varying frequencies.

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We propose and experimentally validate a first-principles based model for the nonlinear piezoelectric response of an electroelastic energy harvester. The analysis herein highlights the importance of modeling inherent piezoelectric nonlinearities that are not limited to higher order elastic effects but also include nonlinear coupling to a power harvesting circuit. Furthermore, a nonlinear damping mechanism is shown to accurately restrict the amplitude and bandwidth of the frequency response. The linear piezoelectric modeling framework widely accepted for theoretical investigations is demonstrated to be a weak presumption for near-resonant excitation amplitudes as low as 0.5 g in a prefabricated bimorph whose oscillation amplitudes remain geometrically linear for the full range of experimental tests performed ͑never exceeding 0.25% of the cantilever overhang length͒. Nonlinear coefficients are identified via a nonlinear least-squares optimization algorithm that utilizes an approximate analytic solution obtained by the method of harmonic balance. For lead zirconate titanate ͑PZT-5H͒, we obtained a fourth order elastic tensor component of c 1111 p = −3.6673ϫ 10 17 N / m 2 and a fourth order electroelastic tensor value of e 3111 = 1.7212 ϫ 10 8 m / V.