Samuel C. Stanton

Reversible hysteresis for broadband magnetopiezoelastic energy harvesting

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.

Nonlinear piezoelectricity in electroelastic energy harvesters: Modeling and experimental identification

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 length). Nonlinear coefficients are identified via a nonlinear least-squares optimization algorithm that utilizes an approximate analytic solution obta...

Nonlinear nonconservative behavior and modeling of piezoelectric energy harvesters including proof mass effects

Nonlinear piezoelectric effects in flexural energy harvesters have recently been demonstrated for drive amplitudes well within the scope of anticipated vibration environments for power generation. In addition to strong softening effects, steady-state oscillations are highly damped as well. Nonlinear fluid damping was previously employed to successfully model drive dependent decreases in frequency response due to the high-velocity oscillations, but this article instead harmonizes with a body of literature concerning weakly excited piezoelectric actuators by modeling nonlinear damping with nonconservative piezoelectric constitutive relations. Thus, material damping is presumed dominant over losses due to fluid-structure interactions. Cantilevers consisted of lead zirconate titanate (PZT)-5A and PZT-5H are studied, and the addition of successively larger proof masses is shown to precipitate nonlinear resonances at much lower base excitation thresholds while increasing the influence of higher-order nonlinearities. Parameter identification results using a multiple scales perturbation solution suggest that empirical trends are primarily due to higher-order elastic and dissipation nonlinearities and that modeling linear electromechanical coupling is sufficient. This article concludes with the guidelines for which utilization of a nonlinear model is preferred.

Resonant manifestation of intrinsic nonlinearity within electroelastic micropower generators

This letter investigates the nonlinear response of a bimorph energy harvester comprised of lead zirconate titanate (PZT-5A) laminates. For near resonant excitations, we demonstrate significant intrinsic nonlinear behavior despite geometrically linear motion. Fourth order elastic and electroelastic tensor values for PZT-5A are identified following methods recently published concerning a PZT-5H bimorph. A response trend indicative of a nonlinear dissipative mechanism is discussed as well as the inadequacy of linear modeling. The PZT-5A bimorph exhibits an increased softening frequency response in comparison to PZT-5H. The results contained herein are also applicable to electroelastic sensor and actuator technologies.

Harvesting Energy From the Nonlinear Oscillations of a Bistable Piezoelectric Inertial Energy Generator

Piezoelectric materials constitute an efficient transduction medium for passive power generation from ambient vibrations. As such, the unimorph and bimorph piezoelectric laminate linear beam is a prolifically researched energy harvesting device. The linear modeling framework is amenable to analytical solutions and frequency matching inertial energy generators to environmental oscillations is a seemingly ideal solution. Realistically, however, environmental disturbances are rarely of one particular frequency and linear oscillators are capable of strong responses only within a limited frequency range about system resonance. In view of these shortcomings, this paper builds upon a new research direction and shift in design philosophy toward purposefully incorporating nonlinearity into energy harvesting systems. In particular, the nonlinear magnetic forces of repulsion are introduced at the free end of a cantilevered bimorph piezoelectric beam, where the separation distance between two opposing permanent magnets doubles as a controllable bifurcation parameter. The numerical results demonstrate the efficacy of the nonlinear responses to yield markedly increased power levels when subject to deterministic excitations of varying forcing frequency and amplitude.Copyright

Passive subharmonic elimination

This paper investigates an approach to passively eliminate subharmonic responses in nonlinear oscillators forced at resonance. A general framework is developed for identifying asymptotic levels where parameter values can be passively tuned to achieve dynamic cancellation of subharmonics. The results apply to oscillators with an arbitrary nonlinear structure. Due to its breadth of application from atomic force microscopy to aeromechanics, the methodology is demonstrated using a reduced-order model for an inextensible cantilevered beam carrying a concentrated mass. The concentrated mass provides a simple opportunity to vary parameters to achieve subharmonic elimination characteristics. Nonlinear simulation results indicate that parameter choices derived from the perturbation scheme are robust for a significant range of forcing amplitudes. Limits of the harmonic elimination and the sensitivity of the result to control parameters are discussed as well.This paper investigates an approach to passively eliminate subharmonic responses in nonlinear oscillators forced at resonance. A general framework is developed for identifying asymptotic levels where parameter values can be passively tuned to achieve dynamic cancellation of subharmonics. The results apply to oscillators with an arbitrary nonlinear structure. Due to its breadth of application from atomic force microscopy to aeromechanics, the methodology is demonstrated using a reduced-order model for an inextensible cantilevered beam carrying a concentrated mass. The concentrated mass provides a simple opportunity to vary parameters to achieve subharmonic elimination characteristics. Nonlinear simulation results indicate that parameter choices derived from the perturbation scheme are robust for a significant range of forcing amplitudes. Limits of the harmonic elimination and the sensitivity of the result to control parameters are discussed as well.

Analysis of the Bistable Piezoelectric Inertial Generator by the Harmonic Balance Method

This paper analytically predicts the existence, stability, and changes due to parameter variations on the different oscillations of a bistable piezoelectric generator. Existing work on this type of system has assumed linear piezoelectric behavior and linear damping and has been confined to numerical studies and experimental explorations. This paper improves upon the previous work by incorporating nonlinear dissipation and cubic softening influences in the electroelastic laminates prior to analytical analysis. This analysis provides a framework for theoretical prediction of a variety of empirical observations including potential well escape and optimum impedance loading.Copyright

Aeroelastic Limit Cycles as a Small Scale Energy Source

Nonlinear limit cycle oscillations of an aeroelastic energy harvester are exploited for enhanced piezoelectric power generation from aerodynamic flows. Specifically, a flexible beam with piezoelectric laminates is excited by a uniform axial flow field in a manner analogous to a flapping flag such that the system delivers power to an electrical impedance load. Fluid-structure interaction is modeled by augmenting a system of nonlinear equations for an electroelastic beam with a discretized vortex-lattice potential flow model. Experimental results from a prototype aeroelastic energy harvester are also presented. Root mean square electrical power on the order of 2.5 mW was delivered below the flutter boundary of the test apparatus at a comparatively low wind speed of 27 m/s and a chord normalized limit cycle amplitude of 0.33. Moreover, subcritical limit cycles with chord normalized amplitudes of up to 0.46 were observed. Calculations indicate that the system tested here was able to access over 17% of the flow energy to which it was exposed. Methods for designing aeroelastic energy harvesters by exploiting nonlinear aeroelastic phenomena and potential improvements to existing relevant aerodynamic models are also discussed.Copyright

On the Manifestation and Influence of Material Nonlinearity in Electroelastic Power Generators

We investigate and model observed nonlinear piezoelectric response of an electroelastic energy harvester. The model employed is a simplified version of the fully nonlinear model proposed by Stanton and Mann [1] since the mechanical oscillations of the experimental device remain in the geometrically linear regime. However, we include quadratic damping due to the appearance of even superharmonics in experimental data as well as suppressed frequency response. 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 PZT-5H, we obtained a fourth order elastic tensor component of cp 1111 = −8.2515 × 1015 N/m2 and a fourth order electroelastic tensor value of e3111 = 9.6816 × 107 m/V.Copyright