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Melnikov theoretic methods for characterizing the dynamics of the bistable piezoelectric inertial generator in complex spectral environments

Publication ,  Journal Article
Stanton, SC; Mann, BP; Owens, BAM
Published in: Physica D: Nonlinear Phenomena
March 15, 2012

Piezoelectric energy harvesters exploiting strong mechanical nonlinearities exhibit intrinsic suitability for one of several modern challenges in vibratory energy harvesting: consistent kinetic performance in the presence of broadband environmental excitation. In particular, the bistable piezoelectric generator has been prolifically examined. However, most of the relevant literature relies on numerical simulation of specific experimental realizations to demonstrate superior performance. Due to the complexities and lack of analytical solutions for such designs, streamlined methods for parameter optimization,potential well shaping, optimal electromechanical coupling considerations, and other design methodologies are thus inhibited. To facilitate future innovation and research, this paper employs techniques from chaotic dynamical systems theory to provide a simplified analytical framework such that deeper insight into the performance of the bistable piezoelectric inertial generator may be obtained. Specifically, Melnikov theory is investigated to provide metrics for which homoclinic bifurcation may occur in the presence of harmonic, multi-frequency, and broadband excitation. The analysis maintains full consideration of the electromechanical coupling and electrical impedance effects and predicts that for range of dimensionless electrical impedance values, the threshold for chaotic motion and other high-energy solutions is significantly influenced.

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Published In

Physica D: Nonlinear Phenomena

DOI

ISSN

0167-2789

Publication Date

March 15, 2012

Volume

241

Issue

6

Start / End Page

711 / 720

Related Subject Headings

  • Fluids & Plasmas
  • 4903 Numerical and computational mathematics
  • 4902 Mathematical physics
  • 4901 Applied mathematics
  • 0102 Applied Mathematics
 

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Stanton, S. C., Mann, B. P., & Owens, B. A. M. (2012). Melnikov theoretic methods for characterizing the dynamics of the bistable piezoelectric inertial generator in complex spectral environments. Physica D: Nonlinear Phenomena, 241(6), 711–720. https://doi.org/10.1016/j.physd.2011.12.010
Stanton, S. C., B. P. Mann, and B. A. M. Owens. “Melnikov theoretic methods for characterizing the dynamics of the bistable piezoelectric inertial generator in complex spectral environments.” Physica D: Nonlinear Phenomena 241, no. 6 (March 15, 2012): 711–20. https://doi.org/10.1016/j.physd.2011.12.010.
Stanton SC, Mann BP, Owens BAM. Melnikov theoretic methods for characterizing the dynamics of the bistable piezoelectric inertial generator in complex spectral environments. Physica D: Nonlinear Phenomena. 2012 Mar 15;241(6):711–20.
Stanton, S. C., et al. “Melnikov theoretic methods for characterizing the dynamics of the bistable piezoelectric inertial generator in complex spectral environments.” Physica D: Nonlinear Phenomena, vol. 241, no. 6, Mar. 2012, pp. 711–20. Scopus, doi:10.1016/j.physd.2011.12.010.
Stanton SC, Mann BP, Owens BAM. Melnikov theoretic methods for characterizing the dynamics of the bistable piezoelectric inertial generator in complex spectral environments. Physica D: Nonlinear Phenomena. 2012 Mar 15;241(6):711–720.
Journal cover image

Published In

Physica D: Nonlinear Phenomena

DOI

ISSN

0167-2789

Publication Date

March 15, 2012

Volume

241

Issue

6

Start / End Page

711 / 720

Related Subject Headings

  • Fluids & Plasmas
  • 4903 Numerical and computational mathematics
  • 4902 Mathematical physics
  • 4901 Applied mathematics
  • 0102 Applied Mathematics