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Research Papers

Effect of Strain Nodes and Electrode Configuration on Piezoelectric Energy Harvesting From Cantilevered Beams

[+] Author and Article Information
A. Erturk1

Center for Intelligent Material Systems and Structures, Department of Engineering Science and Mechanics, Virginia Tech, Blacksburg, VA 24061erturk@vt.edu

P. A. Tarazaga, J. R. Farmer, D. J. Inman

Center for Intelligent Material Systems and Structures, Department of Mechanical Engineering, Virginia Tech, Blacksburg, VA 24061

The abbreviation PZT is used here for a generic piezoelectric ceramic, rather than a specific material.

The effect of a tip mass is discussed in Sec. 2.

It is assumed in the entire analysis that the width of the electrodes is identical to that of the PZT.

The dominating term in Eq. 18 for $Mt∕mL→∞$ is the characteristic equation of a clamped-pinned beam: $tanhλ−tanλ=0$ (because the system is positive definite, $λ≠0$ in the dominating term).

1

Corresponding author.

J. Vib. Acoust 131(1), 011010 (Jan 06, 2009) (11 pages) doi:10.1115/1.2981094 History: Received October 25, 2007; Revised July 03, 2008; Published January 06, 2009

Abstract

For the past five years, cantilevered beams with piezoceramic layer(s) have been frequently used as piezoelectric energy harvesters for vibration-to-electric energy conversion. Typically, the energy harvester beam is located on a vibrating host structure and the dynamic strain induced in the piezoceramic layer(s) results in an alternating voltage output across the electrodes. Vibration modes of a cantilevered piezoelectric energy harvester other than the fundamental mode have certain strain nodes where the dynamic strain distribution changes sign in the direction of beam length. It is theoretically explained and experimentally demonstrated in this paper that covering the strain nodes of vibration modes with continuous electrodes results in strong cancellations of the electrical outputs. A detailed dimensionless analysis is given for predicting the locations of the strain nodes of a cantilevered beam in the absence and presence of a tip mass. Since the cancellation issue is not peculiar to clamped-free boundary conditions, dimensionless data of modal strain nodes are tabulated for some other practical boundary condition pairs and these data can be useful in modal actuation problems as well. How to avoid the cancellation problem in energy harvesting by using segmented electrode pairs is described for single-mode and multimode vibrations of a cantilevered piezoelectric energy harvester. An electrode configuration-based side effect of using a large tip mass on the electrical response at higher vibration modes is discussed theoretically and demonstrated experimentally.

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Figures

Figure 1

Piezoelectric energy harvester under translational and small rotational base excitations

Figure 2

(a) Normalized displacement and (b) normalized strain mode shapes of a cantilevered beam without a tip mass for the first three vibration modes

Figure 3

Variation of the (a) normalized displacement and (b) normalized strain mode shapes of the second vibration mode with tip mass-to-beam mass ratio

Figure 4

(a) Variation of the strain node positions of the second and the third vibration modes and (b) variation of the first five frequency numbers with tip mass-to-beam mass ratio

Figure 5

Experimental setup for demonstration of the effect of strain nodes on the voltage output

Figure 6

Voltage histories for excitation at the first natural frequency of the beam: (a) PZT1, (b) PZT2, and (c) PZT3 along with the maximum response obtained by combining PZT1 and PZT2

Figure 7

Voltage histories for excitation at the second natural frequency of the beam: (a) PZT1, (b) PZT2, and (c) PZT3 along with the maximum response obtained by combining PZT1 and PZT2

Figure 8

Continuous and segmented electrode configurations with full-wave rectifiers: (a) suitable for mode 1 excitation, (b) suitable for mode 2 excitation, and (c) suitable for both mode 1 and mode 2 excitations

Figure 9

Piezoelectric bimorph and its experimental base excitation with a shaker in clamped-free boundary conditions: (a) without a tip mass and (b) with a tip mass

Figure 10

Experimental comparison of the (a) tip displacement and (b) electrical power FRFs of the bimorph cantilever configurations with and without the tip mass

Errata

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