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Research Papers

Analysis of Piezoelectric Energy Harvesters of a Moderate Aspect Ratio With a Distributed Tip Mass

[+] Author and Article Information
Jae Eun Kim

Faculty of Mechanical and Automotive Engineering, Catholic University of Daegu, Geumnak 5-ro, Hayang-eup, Gyeongsan-si, Gyeongbuk 712-702, Republic of Korea

Yoon Young Kim1

National Creative Research Initiatives Center for Multiscale Design, Advanced Automotive Research Center, School of Mechanical and Aerospace Engineering, Seoul National University, 599 Gwanak-ro, Gwanak-gu, Seoul 151-744, Republic of Koreayykim@snu.ac.kr

1

Corresponding author.

J. Vib. Acoust 133(4), 041010 (Apr 08, 2011) (16 pages) doi:10.1115/1.4003598 History: Received December 09, 2009; Revised December 06, 2010; Published April 08, 2011; Online April 08, 2011

Various mathematical beam models have been proposed for the efficient analysis of a piezoelectric energy harvester (PEH) and carrying out parameter study but there appears no beam model suitable for a PEH of a moderate width-to-length aspect ratio with a distributed tip mass, and so, moderate width-to-length aspect ratios and distribution effects of a tip mass over a finite length will be mainly focused on in the present beam analysis. To deal with a wide range of aspect ratios, the material coefficients appearing in the constitutive equations of a PEH beam will be interpolated by those of the limiting plane-strain and plane-stress conditions. The key idea in the interpolation is to derive the interpolation parameter analytically by using the fundamental frequency of a cantilevered beam of moderate aspect ratios. To deal with the distribution effects of a tip mass over a finite length, the use of a set of polynomial deflection shape functions is proposed in the assumed mode approach. The equations to predict the electrical outputs based on the proposed enhanced beam model are explicitly expressed in template forms, so one can calculate the outputs easily from the forms. The validity and accuracy were checked for unimorph and bimorph PEHs by comparing the results from the developed beam model, the conventional beam model, and a three-dimensional finite element model. The comparisons showed substantial improvements by the developed model in predicting the electrical outputs.

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Copyright © 2011 by American Society of Mechanical Engineers
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Figures

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Figure 10

Comparative analysis in the case of a unimorph configuration with a distributed tip mass: (a) open-circuit voltage, (b) output voltage and power at the short-circuit resonant frequency, and (c) output voltage and power at the open-circuit resonant frequency

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Figure 11

Comparative analysis in the case of a bimorph configuration in parallel with a distributed tip mass: (a) open-circuit voltage, (b) output voltage and power at the short-circuit resonant frequency, and (c) output voltage and power at the open-circuit resonant frequency

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Figure 1

(a) The unimorph configuration of a piezoelectric composite energy harvester and (b) the cross-sectional shape of this configuration (The locations of top and bottom surfaces of the substrate and piezoelectric materials as well as the poling direction for the piezoelectric material are shown.)

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Figure 2

(a) The bimorph configuration of a piezoelectric composite energy harvester and (b) the cross-sectional shape of this configuration in series and parallel (The locations of top and bottom surfaces of the substrate and piezoelectric materials as well as the poling direction for the piezoelectric material are shown.)

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Figure 3

Beam models used to represent cantilevered piezoelectric energy harvesters with (a) a distributed tip mass mounted at the end of the beam, (b) a concentrated tip mass, and (c) a distributed tip mass attached to the end of the beam

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Figure 4

A unimorph piezoelectric energy harvester with a tip mass under uniformly distributed loads that simulate the inertial force of the beam qB and a tip mass qM

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Figure 5

Resonant frequencies of a unimorph piezoelectric energy harvester that are obtained for various aspect ratios (b/L) by using the proposed constitutive equations, the plane-strain and plane-stress conditions in the distributed parameter model, and the 3D FEA through ANSYS : (a) short-circuit and (b) open-circuit

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Figure 6

The case of a unimorph configuration without a tip mass (b/L=1): (a) open-circuit voltage, (b) output voltage and power at the short-circuit resonant frequency, and (c) output voltage and power at the open-circuit resonant frequency (The results are obtained by the four methods explained with respect to Fig. 5.)

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Figure 7

A bimorph piezoelectric energy harvester in series with various aspect ratios (b/L): (a) short-circuit resonant frequencies and (b) open-circuit resonant frequencies

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Figure 8

The case of a bimorph configuration in series without a tip mass (b/L=1): (a) open-circuit voltage, (b) output voltage and power at the short-circuit resonant frequency, and (c) output voltage and power at the open-circuit resonant frequency

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Figure 9

Results of a unimorph configuration without a tip mass compared with those in Ref. 21: (a) output voltage and power at the short-circuit resonant frequency and (b) output voltage and power at the open-circuit resonant frequency

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