Global nonlinear distributed-parameter model of parametrically excited piezoelectric energy harvesters

A. Abdelkefi, A. H. Nayfeh, M. R. Hajj

Research output: Contribution to journalArticlepeer-review

167 Scopus citations

Abstract

A global nonlinear distributed-parameter model for a piezoelectric energy harvester under parametric excitation is developed. The harvester consists of a unimorph piezoelectric cantilever beam with a tip mass. The derived model accounts for geometric, inertia, piezoelectric, and fluid drag nonlinearities. A reduced-order model is derived by using the Euler-Lagrange principle and Gauss law and implementing a Galerkin discretization. The method of multiple scales is used to obtain analytical expressions for the tip deflection, output voltage, and harvested power near the first principal parametric resonance. The effects of the nonlinear piezoelectric coefficients, the quadratic damping, and the excitation amplitude on the output voltage and harvested electrical power are quantified. The results show that a one-mode approximation in the Galerkin approach is not sufficient to evaluate the performance of the harvester. Furthermore, the nonlinear piezoelectric coefficients have an important influence on the harvester's behavior in terms of softening or hardening. Depending on the excitation frequency, it is determined that, for small values of the quadratic damping, there is an overhang associated with a subcritical pitchfork bifurcation.

Original languageEnglish
Pages (from-to)1147-1160
Number of pages14
JournalNonlinear Dynamics
Volume67
Issue number2
DOIs
StatePublished - Jan 2012

Keywords

  • Distributed parameter model
  • Energy harvesting
  • Method of multiple scales
  • Nonlinear analysis
  • Piezoelectric material

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