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Research Papers

Generalized Solutions of Piezoelectric Vibration-Based Energy Harvesting Structures Using an Electromechanical Transfer Matrix Method

[+] Author and Article Information
Timothy Reissman

Department of Mechanical and
Aerospace Engineering,
Cornell University,
226 Upson Hall,
Ithaca, NY 14853
e-mail: tr34@cornell.edu

Adam Wickenheiser

Department of Mechanical and
Aerospace Engineering,
George Washington University,
800 22nd Street, NW Suite 729,
Washington, DC 20052
e-mail: amwick@gwu.edu

Ephrahim Garcia

Department of Mechanical and
Aerospace Engineering,
Cornell University,
224 Upson Hall,
Ithaca, NY 14853
e-mail: eg84@cornell.edu

Contributed by the Technical Committee on Vibration and Sound of ASME for publication in the JOURNAL OF VIBRATION AND ACOUSTICS. Manuscript received February 7, 2014; final manuscript received March 10, 2016; published online May 4, 2016. Assoc. Editor: Mohammed Daqaq.

J. Vib. Acoust 138(4), 041001 (May 04, 2016) (12 pages) Paper No: VIB-14-1042; doi: 10.1115/1.4033261 History: Received February 07, 2014; Revised March 10, 2016

Piezoelectric vibration-based energy harvesting (pVEH) offers much potential as renewable energy structures. Within the literature, often geometry-specific models are developed, making designs of new structures difficult. In this work, a generalized linear algebraic method is developed. The method incorporates the transfer matrix method (TMM) into the well-accepted distributed parameter electromechanical model for a composite-piezoelectric, Euler–Bernoulli beam. The result is an electromechanical TMM which is highly accurate at predicting both structural and energy harvesting performances for a wide variety of designs which have chainlike topologies. A simplification is made within the method to model structures which operate solely within bending modes, reducing the computation to analyses of only four-by-four state transition matrices, regardless of structural complexity. As many applications aim to optimize the large bending mode piezoelectric effect, this simplification does not limit the versatility of the method. To demonstrate the validity of this statement, comparisons were performed to evaluate the accuracy of the method's predictions for six piezoelectric topologies, including a unimorph without a tip mass, a bimorph with a tip mass, several partial-length bimorphs without a tip mass, and three different multibeam bimorph structures with inline and folded-back designs. The results show differences no greater than 2.24% for the first and second natural frequencies of the structures. Likewise, the method yields excellent predictions for the mode shapes, their slopes, and the voltage frequency responses, especially within the ±10% bounds of the natural frequencies. Thus, the future design of new structures is shown to be simplified using this generalizable method.

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References

Figures

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Fig. 1

pVEH (D220-A4-103, Piezo Systems Inc.) and its TMM representation

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Fig. 2

Forces and moments along the jth prismatic beam segment

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Fig. 3

Folded-back pVEH structures and their TMM representations: (a) without a tip mass and (b) with a tip mass

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Fig. 4

Forces and moments on a lumped mass located at x=Lj

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Fig. 6

Partial-length bimorph and its TMM representation

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Fig. 5

TMM representation of two common pVEH structures: (a) unimorph without a tip mass and (b) bimorph with a tip mass

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Fig. 8

First mode shape slopes comparison of TMM with experiments for partial-length bimorphs

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Fig. 7

First mode shape comparison of TMM with experiments for partial-length bimorphs

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Fig. 9

Voltage frequency response comparison of TMM with experiment for inline, bimorph beam with a beam adhered to the tip

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Fig. 10

Voltage frequency response comparison of TMM with experiment for folded-back, bimorph beams without an added tip mass

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Fig. 11

Voltage frequency response comparison of TMM with experiment for folded-back, bimorph beams with an added tip mass

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