Research Papers

Analytical Modeling and Experimental Verification of the Vibrations of the Zigzag Microstructure for Energy Harvesting

[+] Author and Article Information
M. Amin Karami1

Center for Intelligent Materials Systems and Structures, Virginia Tech, 310 Durham Hall, Blacksburg, VA 24061karami@vt.edu

Daniel J. Inman

Center for Intelligent Materials Systems and Structures, Virginia Tech, 310 Durham Hall, Blacksburg, VA 24061


Corresponding author.

J. Vib. Acoust 133(1), 011002 (Dec 08, 2010) (10 pages) doi:10.1115/1.4002783 History: Received December 15, 2009; Revised May 31, 2010; Published December 08, 2010; Online December 08, 2010

This paper addresses an issue in energy harvesting that has plagued the potential use of harvesting through the piezoelectric effect at the micro-electro-mechanical systems (MEMS) scale. Effective energy harvesting devices typically consist of a cantilever beam substrate coated with a thin layer of piezoceramic material and fixed with a tip mass tuned to resonant at the dominant frequency of the ambient vibration. The fundamental natural frequency of a beam increases as its length decreases, so that at the MEMS scale the resonance condition occurs orders of magnitude higher than ambient vibration frequencies, rendering the harvester ineffective. Here, we propose a new geometry for MEMS scale cantilever harvesters with low fundamental frequencies. A “zigzag” geometry is proposed, modeled, and solved to show that such a structure would be able to vibrate near resonance at the MEMS scale. An analytical solution is presented and verified against Rayleigh’s method and is validated against a macroscale experiment. The analysis is used to provide design guidelines and parametric studies for constructing an effective MEMS scale energy harvesting device in the frequency range common to low frequency ambient vibrations, removing a current barrier.

Copyright © 2011 by American Society of Mechanical Engineers
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Figure 1

The zigzag energy harvesting structure

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Figure 2

Bending moment diagrams for (a) cantilevered beam and (b) zigzag structure

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Figure 3

Equilibrium and compatibility conditions

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Figure 4

Natural frequency relation with the number of members

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Figure 5

(a)–(h) Mass normalized mode shapes of the first four modes

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Figure 6

(a) and (b) Mode shape of the tenth mode

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Figure 7

The exact versus the approximate fundamental frequencies

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Figure 8

Experimental zigzag structures

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Figure 9

Analytical predictions versus experimental measurements




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