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Technical Briefs

Performance of Mechanical Bandpass Filters Used in Energy Scavenging in the Presence of Fabrication Errors and Coupling

[+] Author and Article Information
S. M. Shahruz

 Berkeley Engineering Research Institute, P.O. Box 9984, Berkeley, CA 94709shahruz@cal.berkeley.edu

J. Vib. Acoust 130(5), 054505 (Aug 19, 2008) (9 pages) doi:10.1115/1.2950056 History: Received March 22, 2007; Revised December 03, 2007; Published August 19, 2008

In this paper, several mathematical models that are more realistic representations of mechanical bandpass filters are studied. Such filters can be used in energy scavengers to convert energy from vibration sources into small amount of electricity. A mechanical bandpass filter is an ensemble of cantilever beams where at the tip of each beam a mass, known as the proof mass, is mounted. A beam with a proof mass at its tip is called a beam-mass system. By studying a variety of models representing the filter dynamics, it will be unraveled to what extent fabrication errors in beam-mass systems of a filter and/or the coupling of such systems can alter the bandpass behavior of a fabricated filter.

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Copyright © 2008 by American Society of Mechanical Engineers
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Figures

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Figure 8

The Bode magnitude plots of the transfer functions corresponding to beam-mass systems in Example 3.3, when such systems are coupled. The peaks of most plots have dropped from −60dB.

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Figure 9

The Bode magnitude plots of the transfer functions corresponding to beam-mass systems in Example 3.4, when such systems are coupled and there are fabrication errors in them.

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Figure 10

The magnification of the Bode magnitude plots in Fig. 1 close to 157Hz. Due to the coupling, the plots of three beam-mass systems have maxima at this frequency, although the maxima are less than −60dB.

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Figure 2

An ensemble of cantilever beams with proof masses at their tips. When dimensions of the beams and masses of the proof masses are chosen appropriately, this ensemble can function as a bandpass filter.

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Figure 1

A typical energy scavenger consists of a cantilever beam on which piezoelectric films and a mass, known as the proof mass, are mounted

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Figure 7

(a) The Bode magnitude plots of the transfer functions corresponding to the beam-mass systems 1, 10, and 19 in Example 3.2. Each beam-mass system has several resonant frequencies; (b) Beam-mass systems such as 1, 2, and 3 that are close to each other can vibrate together at an excitation frequency.

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Figure 6

The Bode magnitude plots of the transfer functions corresponding to beam-mass systems in Example 3.2, when such systems are coupled. The peaks of most plots have dropped from −60dB.

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Figure 5

The Bode magnitude plots of the transfer functions corresponding to beam-mass systems of the device in Fig. 2, when there are fabrication errors in such systems. The fabricated device functions as a bandpass filter, although its frequency band has shifted.

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Figure 4

The Bode magnitude plots of the transfer functions corresponding to the designed beam-mass systems of the device in Fig. 2, where fabrication errors in beam-mass systems and/or the coupling of such systems are absent. The device functions as a bandpass filter.

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Figure 3

A schematic of the ith beam with a proof mass at its tip. The vibration source exerts the acceleration ü(⋅). The transversal displacement of the beam at an x∊[0,li] and a t⩾0 is denoted by yi(x,t).

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