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Research Papers

Modeling and Characterization of a Piezoelectric Energy Harvester Under Combined Aerodynamic and Base Excitations

[+] Author and Article Information
Amin Bibo

Nonlinear Vibrations and Energy
Harvesting Laboratory (NOVEHL),
Department of Mechanical Engineering,
Clemson University,
Clemson, SC 29634

Abdessattar Abdelkefi

Department of Mechanical
and Aerospace Engineering,
New Mexico State University,
Las Cruces, NM 88003

Mohammed F. Daqaq

Nonlinear Vibrations and Energy
Harvesting Laboratory (NOVEHL),
Department of Mechanical Engineering,
Clemson University,
Clemson, SC 29634
Visiting Associate Professor
Department of Mechanical and Materials
Engineering,
Masdar Institute of Science and Technology (MIST),
Abu Dhabi, UAE
e-mails: mdaqaq@clemson.edu;
mfdaqaq@masdar.ac.ae

Contributed by the Technical Committee on Vibration and Sound of ASME for publication in the JOURNAL OF VIBRATION AND ACOUSTICS. Manuscript received March 3, 2014; final manuscript received January 4, 2015; published online February 18, 2015. Assoc. Editor: Marco Amabili.

J. Vib. Acoust 137(3), 031017 (Jun 01, 2015) (12 pages) Paper No: VIB-14-1068; doi: 10.1115/1.4029611 History: Received March 03, 2014; Revised January 04, 2015; Online February 18, 2015

This paper develops and validates an aero-electromechanical model which captures the nonlinear response behavior of a piezoelectric cantilever-type energy harvester under combined galloping and base excitations. The harvester consists of a thin piezoelectric cantilever beam clamped at one end and rigidly attached to a bluff body at the other end. In addition to the vibratory base excitations, the beam is also subjected to aerodynamic forces resulting from the separation of the incoming airflow on both sides of the bluff body which gives rise to limit-cycle oscillations when the airflow velocity exceeds a critical value. A nonlinear electromechanical distributed-parameter model of the harvester under the combined excitations is derived using the energy approach and by adopting the nonlinear Euler–Bernoulli beam theory, linear constitutive relations for the piezoelectric transduction, and the quasi-steady assumption for the aerodynamic loading. The resulting partial differential equations of motion are discretized and a reduced-order model is obtained. The mathematical model is validated by conducting a series of experiments at different wind speeds and base excitation amplitudes for excitation frequencies around the primary resonance of the harvester. Results from the model and experiment are presented to characterize the response behavior under the combined loading.

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Figures

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Fig. 1

Schematic of a piezoelectric vibratory energy harvester and the associated linear frequency response (Ω: excitation frequency, ω0: resonant frequency, R: electric load, and V: output voltage)

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Fig. 2

Different mechanisms of flow energy harvesting: (a) vortex-induced vibrations (fv.s: vortex shedding frequency and f0: resonant frequency), (b) flutter (U: wind speed and Uf: flutter speed), and (c) galloping (U: wind speed and Ug: galloping speed)

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Fig. 3

A schematic diagram of the energy harvester and piezoelectric beam section

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Fig. 4

Deformation of a differential beam element

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Fig. 5

Tip body cross section in flow

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Fig. 6

A view of the experimental setup

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Fig. 7

Variation of the RMS tip deflection with (a) wind speed: single-mode approximation (solid) and a three-mode reduced-order model (dashed) and (b) excitation frequency for a base excitation of 0.08 m/s2: theoretical (solid-line) and experimental (asterisks)

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Fig. 8

Variation with wind speed: (a) the steady-state RMS amplitude of the beam tip deflection and output voltage and (b) the response frequency and the effective damping. Asterisks represent experimental data.

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Fig. 9

Variation of the theoretical harvester response with the excitation frequency for different wind speeds below the onset speed of galloping: (a) RMS tip deflection and (b) RMS output voltage

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Fig. 10

Variation of the experimental harvester response with the excitation frequency for different wind speeds below the onset speed of galloping: (a) RMS tip deflection and (b) RMS output voltage

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Fig. 11

Variation of the theoretical harvester response with the excitation frequency for different wind speeds above the onset speed of galloping: (a) RMS tip deflection and (b) RMS output voltage. Top axis represents the ratio Ω/ω1. Solid line represents response from the combined loading while dashed line represents the response from galloping excitation only.

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Fig. 12

Variation of the experimental harvester response with the excitation frequency for different wind speeds above the onset speed of galloping: (a) RMS tip deflection and (b) RMS output voltage. Top axis represents the ratio Ω/ω1. Solid line represents response from the combined loading while dashed line represents the response from galloping excitation only.

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Fig. 13

Experimental time histories, phase portraits, and power spectra of the harvester at points (1)–(7) shown in Fig. 12(a)

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Fig. 14

Variation of the harvester response with the excitation frequency at constant wind speed of 3.8 m/s and different base acceleration amplitudes: (a) RMS tip deflection and (b) RMS output voltage

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Fig. 15

Variation of the RMS tip deflection and output voltage with the base excitation at a constant wind speed of 3.8 m/s and different excitation frequencies: (a) numerical and (b) experimental

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