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Journal of Applied Physics / Volume 108 / Issue 7 / ARTICLES / Interdisciplinary and General Physics

J. Appl. Phys. 108, 074903 (2010); http://dx.doi.org/10.1063/1.3486519 (9 pages)

Nonlinear piezoelectricity in electroelastic energy harvesters: Modeling and experimental identification

Samuel C. Stanton1, Alper Erturk2, Brian P. Mann1, and Daniel J. Inman2

1Department of Mechanical Engineering, Nonlinear Dynamical Systems Laboratory, Duke University, Durham, North Carolina 27708, USA
2Department of Mechanical Engineering, Center for Intelligent Material Systems and Structures, Virginia Tech, Blacksburg, Virginia 24061, USA

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(Received 8 June 2010; accepted 7 August 2010; published online 5 October 2010)

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 obtained by the method of harmonic balance. For lead zirconate titanate (PZT-5H), we obtained a fourth order elastic tensor component of c1111p = −3.6673×1017 N/m2 and a fourth order electroelastic tensor value of e3111 = 1.7212×108 m/V.

© 2010 American Institute of Physics

Article Outline

  1. INTRODUCTION
  2. THEORETICAL MODELING
    1. Nonlinear electroelastic energy expressions
    2. Derivation of the governing nonlinear partial differential equations
    3. Distributed parameters model
  3. EXPERIMENTAL INVESTIGATION
    1. Parameter identification
  4. SUMMARY AND CONCLUSIONS

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KEYWORDS and PACS

Keywords

ab initio calculations, cantilevers, damping, energy harvesting, hydrogen, lead compounds, optimisation, piezoelectric devices, piezoelectricity

PACS

  • 84.60.-h

    Direct energy conversion and storage

  • 88.05.-b

    Energy analysis

  • 77.65.Bn

    Piezoelectric and electrostrictive constants

  • 62.40.+i

    Anelasticity, internal friction, stress relaxation, and mechanical resonances

  • 02.60.Pn

    Numerical optimization

  • 85.50.-n

    Dielectric, ferroelectric, and piezoelectric devices

ARTICLE DATA

Digital Object Identifier
http://dx.doi.org/10.1063/1.3486519

PUBLICATION DATA

ISSN

0021-8979 (print)  
1089-7550 (online)

Publisher

$abstract.society.value is a Member of CrossRef American Institute of Physics

For access to fully linked references, you need to log in.
    F. Cottone, H. Vocca, and L. Gammaitoni, Phys. Rev. Lett. 102, 080601 (2009).

    L. Gammaitoni, I. Neri, and H. Vocca, Appl. Phys. Lett. 94, 164102 (2009)APPLAB000094000016164102000001.

    S. Stanton, C. McGehee, and B. Mann, Appl. Phys. Lett. 95, 174103 (2009)APPLAB000095000017174103000001.

    A. Erturk, J. Hoffmann, and D. Inman, Appl. Phys. Lett. 94, 254102 (2009)APPLAB000094000025254102000001.

    H. Tiersten, J. Appl. Phys. 74, 3389 (1993)JAPIAU000074000005003389000001.

    K. Wolf and O. Gottlieb, J. Appl. Phys. 91, 4701 (2002)JAPIAU000091000007004701000001.

    T. Usher and A. Sim, J. Appl. Phys. 98, 064102 (2005)JAPIAU000098000006064102000001.

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