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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.

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References

Figures

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Fig. 1

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

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Fig. 2

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

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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.

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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

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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.

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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.

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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.

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Fig. 5

Photographs of the prototype

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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.

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Fig. 10

Schematic view of the five layers problem

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