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TECHNICAL PAPERS

An Experimentally Verified Model of a Membrane Mirror Strip Actuated Using a Piezoelectric Bimorph

[+] Author and Article Information
Jamil M. Renno1

Center of Intelligent Material Systems and Structures, Department of Mechanical Engineering, Virginia Polytechnic Institute and State University, Blacksburg, VA 24061-0261renno@vt.edu

Daniel J. Inman

Center of Intelligent Material Systems and Structures, Department of Mechanical Engineering, Virginia Polytechnic Institute and State University, Blacksburg, VA 24061-0261dinman@vt.edu

1

Corresponding author.

J. Vib. Acoust 129(5), 631-640 (Sep 19, 2006) (10 pages) doi:10.1115/1.2756843 History: Received June 08, 2006; Revised September 19, 2006

The behavior of a membrane mirror strip actuated using a piezoelectric bimorph is treated. An improved model for the transverse vibration is presented. The model accounts for the changes in physical properties of the membrane strip at the location of the piezoelectric bimorph. The membrane strip is modeled as a pinned-pinned beam under tension and the finite element method (FEM) is used to represent the system mathematically. The beam under tension assumption allows accounting for the traveling wave effect experienced by a membrane strip and the added flexural rigidity induced by the piezoelectric bimorph. Additionally, the structural and air damping effects are included in the model. An experimental setup is built to verify the proposed model. The frequency response obtained from the proposed model is shown to be in agreement with conducted experiments. Furthermore, the importance of including local mass and stiffness effects is demonstrated.

Copyright © 2007 by American Society of Mechanical Engineers
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References

Figures

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Figure 13

First natural frequency versus tension

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Figure 14

Finite element versus experimental frequency response without accounting for the piezoelectric

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Figure 15

Frequency response measured in ambient and vacuum environments

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Figure 12

Error of the first three natural frequencies at various tensile loads (measured at 9.1cm)

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Figure 11

Bending mode shapes

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Figure 10

Torsional mode at 54.9Hz

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Figure 9

Grid of measurement points

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Figure 8

Schematic of experimental setup using scanning vibrometer

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Figure 7

Frequency response at different measurement points (13.5N tension)

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Figure 6

Coherence of the experimental frequency response (tension is 13.5N, measurement point at 9.1cm from the left boundary)

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Figure 5

Finite element model versus experimental frequency response (tension is 13.5N, measurement point at 9.1cm from the left boundary)

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Figure 4

Picture of the experimental setup

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Figure 3

Schematic of experimental setup using laser vibrometer

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Figure 2

Cubic B-splines extending over five nodes with pinned-pinned boundary conditions

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Figure 1

Schematic of the membrane strip with piezoelectric bimorph

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