### 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 language | English (US) |
---|---|

Pages (from-to) | 577-592 |

Number of pages | 16 |

Journal | Journal of Intelligent Material Systems and Structures |

Volume | 22 |

Issue number | 6 |

DOIs | |

State | Published - Apr 1 2011 |

### Fingerprint

### Keywords

- aeroelasticity.
- energy harvesting
- piezoelectric

### ASJC Scopus subject areas

- Materials Science(all)
- Mechanical Engineering

### Cite this

*Journal of Intelligent Material Systems and Structures*,

*22*(6), 577-592. https://doi.org/10.1177/1045389X11400929

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

Research output: Contribution to journal › Article

*Journal of Intelligent Material Systems and Structures*, vol. 22, no. 6, pp. 577-592. https://doi.org/10.1177/1045389X11400929

}

TY - JOUR

T1 - Electromechanical modeling and normal form analysis of an aeroelastic micro-power generator

AU - Bibo, Amin

AU - Gang Li, Li

AU - Daqaq, Mohammed

PY - 2011/4/1

Y1 - 2011/4/1

N2 - 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.

AB - 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.

KW - aeroelasticity.

KW - energy harvesting

KW - piezoelectric

UR - http://www.scopus.com/inward/record.url?scp=79957487811&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=79957487811&partnerID=8YFLogxK

U2 - 10.1177/1045389X11400929

DO - 10.1177/1045389X11400929

M3 - Article

AN - SCOPUS:79957487811

VL - 22

SP - 577

EP - 592

JO - Journal of Intelligent Material Systems and Structures

JF - Journal of Intelligent Material Systems and Structures

SN - 1045-389X

IS - 6

ER -