0
Research Papers

Design of a Circular Clamped Plate Excited by a Voice Coil and Piezoelectric Patches Used as a Loudspeaker

[+] Author and Article Information
Olivier Doaré

ENSTA-Paristech,
UME, Boulevard des Maréchaux,
Palaiseau Cedex 91762, France
e-mail: olivier.doare@ensta-paristech.fr

Gérald Kergourlay

Canon Research Centre France S.A.S,
Rue de la Touche-Lambert,
Cesson Sevigne 35510, France

Clément Sambuc

ENSTA-Paristech, UME,
Boulevard des Maréchaux,
Palaiseau Cedex 91762, France

1Corresponding author.

Contributed by the Noise Control and Acoustics Division of ASME for publication in the JOURNAL OF VIBRATION AND ACOUSTICS. Manuscript received July 20, 2012; final manuscript received March 21, 2013; published online June 18, 2013. Assoc. Editor: Lonny Thompson.

J. Vib. Acoust 135(5), 051025 (Jun 18, 2013) (13 pages) Paper No: VIB-12-1204; doi: 10.1115/1.4024215 History: Received July 20, 2012; Revised March 21, 2013

In this article, a dynamical model of the vibrations and acoustic radiation of a circular clamped plate excited by a voice coil and two annular piezoelectric patches is derived. This model is used to perform an optimization of the geometries with the objective to minimize the vibration of the plate along its second and third modes, so that the plate's radiation is equilibrated between its first and fourth eigenfrequencies. Experiments are then performed and show a good agreement with the model. Radiation of the designed system presents improvements when compared to a system when only a voice coil is used.

FIGURES IN THIS ARTICLE
<>
Copyright © 2013 by ASME
Your Session has timed out. Please sign back in to continue.

References

Thiele, N., 1971, “Loudspeakers in Vented Boxes: Part 1,” J. Audio Eng. Soc., 19, pp. 181–191.
Thiele, N., 1971, “Loudspeakers in Vented Boxes: Part 2,” J. Audio Eng. Soc., 19(6), pp. 471–483.
Small, R. H., 1972, “Closed-Box Loudspeaker Systems—Part 1: Analysis,” J. Audio Eng. Soc., 20(10), pp. 798–808.
Small, R. H., 1973, “Closed-Box Loudspeaker Systems—Part 2: Synthesis,” J. Audio Eng. Soc., 21(1), pp. 11–18.
Kuo, D., Shiah, Y. C., and Huang, J. H., 2011, “Modal Analysis of a Loudspeaker and Its Associated Acoustic Pressure Field,” ASME J. Vib. Acoust., 133(3), p. 031015. [CrossRef]
Bédard, M., and Berry, A., 2008, “Development of a Directivity-Controlled Piezoelectric Transducer for Sound Reproduction,” J. Sound Vib., 311(3-5), pp. 1271–1285. [CrossRef]
Prokofieva, E., Horoshenkov, K. V., and Harris, N., 2002, “Intensity Measurements of the Acoustic Emission From a DML Panel,” 112th Audio Engineering Society Convention, München, Germany, May 10–13.
Zhang, S., Shen, Y., Shen, X., and Zhou, J., 2006, “Model Optimization of Distributed-Mode Loudspeaker Using Attached Masses,” J. Audio Eng. Soc., 54(4), pp. 295–305.
Berkhout, A. J., 1993, “Acoustic Control by Wave Field Synthesis,” J. Acoust. Soc. Am., 93(5), pp. 2764–2778. [CrossRef]
Pueo, B., López, J. J., Escolano, J., and Hörchens, L., 2010, “Multiactuator Panels for Wave Field Synthesis: Evolution and Present Developments,” J. Audio Eng. Soc., 58(12), pp. 1045–1063.
Alper, S., and Magrab, E. B., 1970, “Radiation From Forced Harmonic Vibrations of a Clamped Circular Plate in an Acoustic Fluid,” J. Acoust. Soc. Am., 48, pp. 681–691. [CrossRef]
Preumont, A., 2002, Vibration Control of Active Structures: An Introduction, 2nd ed., Kluwer Academic, Dordrecht, The Netherlands.
Lin, Y. H., and Chu, C. L., 1996, “Active Flutter Control of a Cantilever Tube Conveying Fluid Using Piezoelectric Actuators,” J. Sound Vib., 196(1), pp. 97–105. [CrossRef]
Block, J. J., and Strganac, W., 1998, “Applied Active Control for a Nonlinear Aeroelastic Structure,” J. Guid. Control, 21(6), pp. 838–845. [CrossRef]
Hagood, N., 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]
Tylikowski, A., 2001, “Control of Circular Plate Vibrations Via Piezoelectric Actuators Shunted With a Capacitive Circuit,” Thin-Walled Struct., 39, pp. 83–94. [CrossRef]
Bisegna, P., Caruso, G., and Maceri, F., 2006, “Optimized Electric Networks for Vibration Damping of Piezoactuated Beams,” J. Sound Vib., 289(4-5), pp. 908–937. [CrossRef]
Anton, S. R., and Sodano, H. A., 2007, “A Review of Power Harvesting Using Piezoelectric Materials (2003-2006),” Smart Mater. Struct., 16, pp. 1–21. [CrossRef]
De Marqui, C., Jr.,Erturk, A., and Inman, D. J., 2009, “An Electromechanical Finite Element Model for Piezoelectric Energy Harvester Plates,” J. Sound Vib., 327(1-2), pp. 9–25. [CrossRef]
Masana, R., and Daqaq, M. F., 2011, “Electromechanical Modeling and Nonlinear Analysis of Axially Loaded Energy Harvesters,” ASME J. Vib. Acoust., 133(1), p. 011007. [CrossRef]
Doaré, O., and Michelin, S., 2011, “Piezoelectric Coupling in Energy-Harvesting Fluttering Flexible Plates: Linear Stability Analysis and Conversion Efficiency,” J. Fluids Struct., 27(8), pp. 1357–1375. [CrossRef]
Fuller, C. R., Hansen, C. H., and Snyder, S. D., 1991, “Experiments on Active Control of Sound Radiation From a Panel Using a Piezoceramic Actuator,” J. Sound Vib., 150(2), pp. 179–190. [CrossRef]
Tzou, H., and Zhou, Y., 1995, “Dynamics and Control of Non-Linear Circular Plates With Piezoelectric Actuators,” J. Sound Vib., 188(2), pp. 189–207. [CrossRef]
Lee, J. C., and Chen, J. C., 1999, “Active Control of Sound Radiation From Rectangular Plates Using Multiple Piezoelectric Actuators,” Appl. Acoust., 57(4), pp. 327–343. [CrossRef]
Chen, K., Chen, G., Pan, H., and Li, S., 2008, “Secondary Actuation and Error Sensing for Active Acoustic Structure,” J. Sound Vib., 309(1–2), pp. 40–51. [CrossRef]
Larbi, W., Deü, J. F., Ciminello, M., and Ohayon, R., 2010, “Structural-Acoustic Vibration Reduction Using Switched Shunt Piezoelectric Patches: A Finite Element Analysis,” ASME J. Vib. Acoust., 132(5), p. 051006. [CrossRef]
Gardonio, P., Bianchi, E., and Elliott, S. J., 2004, “Smart Panel With Multiple Decentralized Units for the Control of Sound Transmission. Part I: Theoretical Predictions,” J. Sound Vib., 274(1–2), pp. 163–192. [CrossRef]
Gardonio, P., Bianchi, E., and Elliott, S. J., 2004, “Smart Panel With Multiple Decentralized Units for the Control of Sound Transmission. Part II: Design of the Decentralized Control Units,” J. Sound Vib., 274(1–2), pp. 193–213. [CrossRef]
Bianchi, E., Gardonio, P., and Elliott, S. J., 2004, “Smart Panel With Multiple Decentralized Units for the Control of Sound Transmission. Part III: Control System Implementation,” J. Sound Vib., 274(1–2), pp. 215–232. [CrossRef]
Lee, C. K., and Moon, F. C., 1989, “Laminated Piezopolymer Plates for Torsion and Bending Sensors and Actuators,” J. Acoust. Soc. Am., 85, pp. 2432–2439. [CrossRef]
Lee, C. K., 1990, “Theory of Laminated Piezoelectric Plates for the Design of Distributed Sensors Actuators. 1. Governing Equations and Reciprocal Relationships,” J. Acoust. Soc. Am., 87, pp. 1144–1158. [CrossRef]
Lee, C. K., and Moon, F. C., 1990, “Modal Sensors/Actuators,” ASME J. Appl. Mech., 57(2), pp. 434–441. [CrossRef]
Pierce, A. D., 1989, Acoustics: An Introduction to Its Physical Principles and Applications, Acoustical Society of America, Melville, NY.
Donoso, A., and Bellido, J. C., 2009, “Distributed Piezoelectric Modal Sensors for Circular Plates,” J. Sound Vib., 319(1–2), pp. 50–57. [CrossRef]
Ducarne, J., Thomas, O., and Deü, J. F., 2012, “Placement and Dimension Optimization of Shunted Piezoelectric Patches for Vibration Reduction,” J. Sound Vib., 331(14), pp. 3286–3303. [CrossRef]
Quaegebeur, N., and Chaigne, A., 2008, “Nonlinear Vibrations of Loudspeaker-like Structures,” J. Sound Vib., 309(1–2), pp. 178–196. [CrossRef]
Mansfield, E. H., 1989, The Bending and Stretching of Plates, 2nd ed., Cambridge University, Cambridge, UK.

Figures

Grahic Jump Location
Fig. 1

Schematic view of a flat-plate loudspeaker with a voice coil and two piezoelectric patches

Grahic Jump Location
Fig. 2

Models of electrical circuits for the voice coil (a) and the piezoelectric patch (b)

Grahic Jump Location
Fig. 3

Typical transfer functions of a clamped flat plate used as a loudspeaker obtained using the present model without considering piezoelectric patches. In dashed blue, N = 1, so that its behavior is similar as a single-mode piston-like loudspeaker. In plain black, N = 5. (a) Voice coil impedance; (b) transfer function between tension at the voice coil outlets and displacement at the center of the plate; (c) transfer function between tension at the voice coil outlets and acceleration at the center of the plate; (d) pressure at 1 m for a voltage of 2.8 V at the voice coil outlets, computed using Rayleigh integral calculation.

Grahic Jump Location
Fig. 4

Contour levels of χp2 in the map (a, b), zeros of χp3 dashed (blue), and zeroes of χc3 plain (red). Points satisfying the criteria of Eq. (45) are indicated by an arrow.

Grahic Jump Location
Fig. 5

Photographs of the prototype

Grahic Jump Location
Fig. 6

Comparison of experimental (dashed blue line) and theoretical (plain black line) transfer functions; (a) voice coil impedance; (b) transfer function between voltage at the voice coil outlets and displacement at the center of the plate; (c) transfer function between voltage at the piezoelectric patches outlets and displacement at the center of the plate when the voice coil outlets are not connected; (d) transfer function between voltage at the piezoelectric patches outlets and displacement at the center of the plate when the voice coil outlets are short-circuited

Grahic Jump Location
Fig. 7

Transfer function between voice coil voltage and displacement at the center of the plate and comparison of noncontrolled system (theory in black plain line, experiment in blue dash-dotted line) and controlled system (theory in green dotted line, experiment in red dashed line). The theoretical case N = 1 is plotted on the same figure with a thin black line to serve as a guide for the eyes representing the ideal case.

Grahic Jump Location
Fig. 8

Transfer function between voice coil voltage and acceleration at the center of the plate and comparison of noncontrolled and controlled systems. Legends are the same as Fig. 7.

Grahic Jump Location
Fig. 9

Power radiated by the plate on axis at 84 cm and comparison of noncontrolled and controlled systems. Experiments in dashed blue and theory in plain black. Grayed region indicates the frequency range where backward radiation interferes with frontward radiation, which is not taken into account by the model. The arrow indicates the bandwidth of the loudspeaker where a maximum 10dB difference between minimum and maximum value is tolerated. (a) Uncontrolled system; (b) controlled system.

Grahic Jump Location
Fig. 10

Schematic view of the five layers problem

Tables

Errata

Discussions

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