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

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
Your Session has timed out. Please sign back in to continue.


Forward, R. L., 1979, “Electronic Damping of Vibrations in Optical Structures,” J. Appl. Opt., 18(5), pp. 690–697. [CrossRef]
Uchino, K., and Ishiii, T., 1988, “Mechanical Damper Using Piezoelectric Ceramics,” J. Ceram. Soc. Jpn., 96(8), pp. 863–867. [CrossRef]
Lesieutre, G. A., and Davis, C. L., 1991, “Frequency-Shaped Passive Damping Using Resistively-Shunted Piezoceramics,” Proceedings of the Conference on Active Materials and Structures, pp. 355–358.
Hagood, N. W., and Crawley, E. F., 1991, “Experimental Investigation of Passive Enhancement of Damping in Space Structures,” J. Guid. Control Dyn., 14(6), pp. 1100–1109. [CrossRef]
Davis, C. L., and Lesieutre, G. A., 2000, “An Actively Tuned Solid-State Vibration Absorber Using Capacitive Shunting of Piezoelectric Stiffness,” J. Sound Vib., 232(3), pp. 601–617. [CrossRef]
Hagood, N. W., and von Flotow, A., 1991, “Damping of Structural Vibrations With Piezoelectric Materials and Passive Electrical Networks,” J. Sound Vib., 146(2), pp. 243–268. [CrossRef]
Wu, S., 1996, “Piezoelectric Shunts With Parallel RL Circuit for Structural Damping and Vibration Control,” Proc. SPIE, 2720, pp. 259–269. [CrossRef]
Wu, S., and Bicos, A. S., 1997, “Structural Vibration Damping Experiments Using Improved Piezoelectric Shunts,” Proc. SPIE, 3045, pp. 40–50. [CrossRef]
Caruso, G., 2001, “A Critical Analysis of Electric Shunt Circuits Employed in Piezoelectric Passive Vibration Damping,” Smart Mater. Struct., 10, pp. 1059–1068. [CrossRef]
Park, C. H., and Inman, D. J., 2003, “Enhanced Piezoelectric Shunt Design,” Shock Vib., 10(2), pp. 127–133.
Clark, W. W., 2000, “Vibration Control With State-Switched Piezoelectric Materials,” J. Intell. Mater. Syst. Struct., 11(4), pp. 263–271. [CrossRef]
Richard, C., Guyomar, D., Audigier, D., and Ching, G., 1999, “Semi-Passive Damping Using Continuous Switching of a Piezoelectric Device,” Proc. SPIE, 3672, pp. 104–111. [CrossRef]
Richard, C., Guyomar, D., Audigier, D., and Bassaler, H., 2000, “Enhanced Semi Passive Damping Using Continuous Switching of a Piezoelectric Device,” Smart Struct. Mater., 3989, pp. 288–299. [CrossRef]
Corr, L., and Clark, W. W., 2002, “Comparison of Low-Frequency Piezoelectric Switching Shunt Techniques for Structural Damping,” Smart Mater. Struct., 11, pp. 370–376. [CrossRef]
Corr, L. R., and Clark, W. W., 2003, “A Novel Semi-Active Multi-Modal Vibration Control Law for a Piezoceramic Actuator,” J. Vib. Acoust., 125, pp. 214–222. [CrossRef]
Collinger, J. C., and Wickert, J. A., 2007, “Adaptive Piezoelectric Vibration Control With Synchronized Switching,” Proceedings of IMECE 2007: 2007 ASME International Mechanical Engineering Congress and Exposition, Seattle, WA, Nov. 11–15, Paper No. IMECE2007-41427, http://dx.doi.org/10.1115/IMECE2007-41427
Collinger, J. C., Wickert, J. A., and Corr, L. R., 2009, “Adaptive Piezoelectric Vibration Control With Synchronized Switching,” ASME J. Dyn. Sys. Meas. and Control, 131, p. 041006. [CrossRef]
Fanson, J. L., and Caughey, T. K., 1990, “Positive Position Feedback Control for Large Space Structures,” AIAA J., 28(4), pp. 717–724. [CrossRef]
Alkhatib, R., and Golnaraghi, M. F., 2003, “Active Structural Vibration Control: A Review,” Shock Vib. Dig., 35(5), pp. 367–383. [CrossRef]
Yan, Y. J., and Yam, L. H., 2002, “Optimal Design of Number and Locations of Actuators in Active Vibration Control of a Space Truss,” Smart Mater. Struct., 11, pp. 496–503. [CrossRef]
Crawley, E. F., and Anderson, E. H., 1990, “Detailed Models of Piezoceramic Actuators of Beams,” J. Intell. Mater. Syst. Struct., 1, pp. 4–25. [CrossRef]
Agrawal, B. N., and Treanor, K. E., 1999, “Shape Control of a Beam Using Piezoelectric Actuators,” Smart Mater. Struct., 8, pp. 729–740. [CrossRef]
Barboni, R., Mannini, A., Fantini, E., and Gaudenzi, P., 2000, “Optimal Placement of PZT Actuators for the Control of Beam Dynamics,” Smart Mater. Struct., 9, pp. 110–120. [CrossRef]
Main, J. A., Garcia, E., and Howard, D., 1994, “Optimal Placement and Sizing of Paired Piezoactuators in Beams and Plates,” Smart Mater. Struct., 3, pp. 373–381. [CrossRef]
Collinger, J. C., Messner, W. C., and Wickert, J. A., 2008, “Vibration Control With Magnetically Mounted Piezoelectric Actuators,” Proceedings of IMECE 2008: 2008 ASME International Mechanical Engineering Congress and Exposition, Boston, MA, Oct. 31–Nov. 6, Paper No. IMECE2008-67369, http://dx.doi.org/10.1115/IMECE2008-67369
Collinger, J. C., 2008, “Adaptive Vibration Control Using Magnetically Mounted Piezoelectric Elements,” Ph.D. thesis, Carnegie Mellon University, Pittsburgh, PA.
Hawwa, M. A., Al-Nassar, Y. N., and Al-Oahtani, H. M., 2011, Piezoelectric Damping Device. Patent Application No. US 2011/0084572 A1.
Tangpong, X. W., Wickert, J. A., and Akay, A., 2008, “Distributed Friction Damping of Traveling Wave Vibration in Rods,” Philos. Trans. R. Soc. London, 366, pp. 811–827. [CrossRef]
Menq, C. H., Bielak, J., and Griffin, J. H., 1986, “The Influence of Microslip on Vibratory Response, Part 1: A New Microslip Model,” J. Sound Vib., 107, pp. 279–293. [CrossRef]
Tangpong, X. W., Wickert, J. A., and Akay, A., 2008, “Finite Element Model for Hysteretic Friction Damper of Traveling Wave Vibration in Axisymmetric Structures,” J. Vib. Acoust., 130(1), p. 011005. [CrossRef]
Girhammer, U. A., and Gopu, V. K. A., 1993, “Composite Beam-Columns With Interlayer Slip—Exact Analysis,” J. Struct. Eng., 119, pp. 1265–1282. [CrossRef]
Heuer, R., and Adam, C., 2000, “Piezoelectric Vibrations of Composite Beams With Interlayer Slip,” Acta Mech., 140, pp. 247–263. [CrossRef]
Wu, Y., Xu, R., and Chen, W., 2007, “Free Vibrations of the Partial-Interaction Composite Members With Axial Force,” J. Sound Vib., 299, pp. 1074–1093. [CrossRef]
Hagood, N. W., Chung, W. H., and von Flotow, A., 1990, “Modelling of Piezoelectric Actuator Dynamics for Active Structural Control,” J. Intell. Mater. Syst. Struct., 1(1), pp. 327–354. [CrossRef]
IEEE, 1988, An American National Standard: IEEE Standard on Piezoelectricity, The Institute of Electrical and Electronics Engineers, Inc., New York, NY.
Becker, E. B., Carey, G. F., and Oden, J. T., 1981, Finite Elements: An Introduction, 1st ed., Vol. 1, Prentice-Hall, Inc., Englewood Cliffs, NJ.
Hollkamp, J. J., and Starchville, T. F., Jr., 1994, “A Self-Tuning Piezoelectric Vibration Absorber,” J. Intell. Mater. Syst. Struct., 5, pp. 559–566. [CrossRef]
Trumper, D. L., Williams, M. E., and Nguyen, T. H., 1993, “Magnet Arrays for Synchronous Motors,” Industry Applications Society Annual Meeting, Conference Record of the IEEE, Vol. 1, pp. 9–18.
Jang, S. M., Lee, S. H., and Jeong, S. S., 2002, “Characteristic Analysis of Eddy-Current Brake System Using the Linear Halbach Array,” IEEE Trans. Magn., 38(5), pp. 2994–2996. [CrossRef]


Grahic Jump Location
Fig. 1

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

Grahic Jump Location
Fig. 2

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

Grahic Jump Location
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

Grahic Jump Location
Fig. 4

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

Grahic Jump Location
Fig. 5

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

Grahic Jump Location
Fig. 6

Experimental setup of cantilever beam with magnetically mounted piezoelectric elements

Grahic Jump Location
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

Grahic Jump Location
Fig. 8

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

Grahic Jump Location
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)

Grahic Jump Location
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

Grahic Jump Location
Fig. 11

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

Grahic Jump Location
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 (*)

Grahic Jump Location
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

Grahic Jump Location
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

Grahic Jump Location
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.

Grahic Jump Location
Fig. 17

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

Grahic Jump Location
Fig. 18

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

Grahic Jump Location
Fig. 15

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




Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In