Electromechanical modeling and normal form analysis of an aeroelastic micro-power generator

Amin Bibo, Li Gang Li, Mohammed Daqaq

Research output: Contribution to journalArticle

Abstract

Combining theories in continuous-systems vibrations, piezoelectricity, and fluid dynamics, we develop and experimentally validate an analytical electromechanical model to predict the response behavior of a self-excited micro-power generator. Similar to music-playing harmonica that create tones via oscillations of reeds when subjected to air blow, the proposed device uses flow-induced self-excited oscillations of a piezoelectric beam embedded within a cavity to generate electric power. To obtain the desired model, we adopt the nonlinear Euler-Bernoulli beam's theory and linear constitutive relationships. We use Hamilton's principle in conjunction with electric circuits theory and the inextensibility condition to derive the partial differential equation that captures the transversal dynamics of the beam and the ordinary differential equation governing the dynamics of the harvesting circuit. Using the steady Bernoulli equation and the continuity equation, we further relate the exciting pressure at the surface of the beam to the beam's deflection, and the inflow rate of air. Subsequently, we employ a Galerkin's descritization to reduce the order of the model and show that a single-mode reduced-order model of the infinite-dimensional system is sufficient to predict the response behavior. Using the method of multiple scales, we develop an approximate analytical solution of the resulting reduced-order model near the stability boundary and study the normal form of the resulting bifurcation. We observe that a Hopf bifurcation of the supercritical nature is responsible for the onset of limit-cycle oscillations.

Original languageEnglish (US)
Pages (from-to)577-592
Number of pages16
JournalJournal of Intelligent Material Systems and Structures
Volume22
Issue number6
DOIs
StatePublished - Apr 1 2011

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Piezoelectricity
Hopf bifurcation
Bifurcation (mathematics)
Networks (circuits)
Circuit theory
Air
Fluid dynamics
Ordinary differential equations
Partial differential equations

Keywords

  • aeroelasticity.
  • energy harvesting
  • piezoelectric

ASJC Scopus subject areas

  • Materials Science(all)
  • Mechanical Engineering

Cite this

Electromechanical modeling and normal form analysis of an aeroelastic micro-power generator. / Bibo, Amin; Gang Li, Li; Daqaq, Mohammed.

In: Journal of Intelligent Material Systems and Structures, Vol. 22, No. 6, 01.04.2011, p. 577-592.

Research output: Contribution to journalArticle

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