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Research Papers

An Investigation Into Using Magnetically Attached Piezoelectric Elements for Vibration Control

[+] Author and Article Information
J. C. Collinger

Bechtel Marine Propulsion Corporation,
West Mifflin, PA, 15122
e-mail: john.c.collinger@gmail.com

W. C. Messner

Department of Mechanical Engineering,
Carnegie Mellon University,
Pittsburgh, PA, 15213

J. A. Wickert

Dean
College of Engineering,
Iowa State University,
Ames, IA, 50011

1Corresponding author.

Contributed by the Technical Committee on Vibration and Sound of ASME for publication in the JOURNAL OF VIBRATION AND ACOUSTICS. Manuscript received February 15, 2011; final manuscript received March 28, 2012; published online October 29, 2012. Assoc. Editor: Ranjan Mukherjee.

J. Vib. Acoust 134(6), 061008 (Oct 29, 2012) (11 pages) doi:10.1115/1.4007021 History: Received February 15, 2011; Revised March 28, 2012

A novel vibration control method utilizing magnetically mounted piezoelectric elements is described. Piezoelectric elements are bonded to permanent magnets, termed here as control mounts, which are attached to the surface of a steel beam through their magnetic attraction. The magnetic-piezoelectric control mounts are an alternative to traditional epoxy attachment methods for piezoelectric elements which allows for easy in-the-field reconfiguration. In model and laboratory measurements, the beam is driven through base excitation and the resonant shunt technique is utilized to demonstrate the attenuation characteristics of two magnetic-piezoelectric control mounts. The coupled system is discretized using a Galerkin finite element model that incorporates the tangential and vertical contact stiffnesses of the beam-magnet interface. The vibration reduction provided by the control mounts using a single magnet are compared to those designed with a magnetic array that alternates the magnetic dipoles along the length of the mount. Even though each design uses the same magnet thickness, the alternating magnetic configuration's interfacial contact stiffness is over 1.5 and 4 times larger in the tangential and vertical directions, respectively, than that of the single magnet, resulting in increased vibration reduction. Measured and simulated results show that the magnetic-piezoelectric control mounts reduced the beam's tip velocity by as much as 3.0 dB and 3.1 dB, respectively. The design tradeoffs that occur when replacing the traditional epoxy layer with a magnet are also presented along with some methods that could improve the vibration reduction performance of the control mounts. This analysis shows that the control mounts attenuate significant vibration despite having an imperfect bond with the beam, thus providing a viable and adaptable alternative to traditional piezoelectric attachment methods.

Copyright © 2012 by ASME
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Figures

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Fig. 1

Illustration of a pinned-free beam, subjected to excitation at the base with torsional stiffness k0 and with magnetically mounted piezoelectric elements

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Fig. 2

Illustration of the (a) interfacial normal and tangential forces and (b) relative axial displacement at the control mount-beam interface

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Fig. 3

The different local elements used in the finite element discretization along with the magnet r and piezoelectric s indices: (a) beam only, (b) beam with only the piezoelectrics, (c) beam with the magnets and piezoelectrics, and (d) beam with only the magnets

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Fig. 4

Schematic of the piezoelectric elements that are connected to a resonant shunt

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Fig. 5

Illustration of experimental setup of cantilever beam with magnetically mounted piezoelectric elements

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Fig. 6

Experimental setup of cantilever beam with magnetically mounted piezoelectric elements

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Fig. 7

Illustration of the the different magnetic arrays: (a) single magnet configuration, and the alternating dipole configurations of the magnets with (b) rectangular and (c) square cross sections

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Fig. 8

The control mounts used in experimentation, illustrating the different magnetic array configurations

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Fig. 9

Illustration of the asymptotic behavior of the (a) third, (b) second, and (c) first bending natural frequencies for different tangential contact stiffnesses per unit length (kv=1×1014N/m2)

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Fig. 10

(a) Illustration of the bending mode shapes, and the (b) third, (c) second, and (d) first bending natural frequencies for different control mount positions along the beam and increasing contact stiffness (kt=kv): simulated (sold lines), single magnet (*), and rectangular (o) configurations

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Fig. 11

Contour plot of the simulated natural frequency percent error for the square magnet configuration

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Fig. 12

(a) Illustration of the beam with the square magnet control mount design, and the (b) third, (c) second, and (d) first bending natural frequencies: simulated (solid lines) and measured (*)

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Fig. 13

The simulated (solid) and measured (dashed) tip velocity of the system with and without resonant shunt control for the three different control mounts

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Fig. 14

Comparison of the simulated maximum relative displacements (solid) to the measured slip parameter (dashed) for the three control mounts: single, rectangular, and square

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Fig. 16

Tip velocity reduction using resonant shunt control for various magnet thicknesses and damping ratios, assuming perfect attachment between magnets and beam. Actual reduction approach zero as magnet thickness, and therefore attraction force, decreases.

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Fig. 17

Illustration of the (a) magnetic dipole configuration of a Halbach array, and (b) natural orientation of magnets

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Fig. 18

Example of a control mount with magnets placed at the ends of the piezoelectric element

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Fig. 15

Tip velocity reduction using resonant shunt control for various contact stiffnesses and damping ratios

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