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TECHNICAL PAPERS

Vibration Control of Toroidal Shells With Parallel and Diagonal Piezoelectric Actuators

[+] Author and Article Information
H. S. Tzou, D. W. Wang

Department of Mechanical Engineering, Structronics Laboratory, University of Kentucky, Lexington, KY 40506-0503

J. Pressure Vessel Technol 125(2), 171-176 (May 05, 2003) (6 pages) doi:10.1115/1.1557635 History: Received December 14, 2001; Revised December 20, 2002; Online May 05, 2003
Copyright © 2003 by ASME
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References

Melo,  F. J. M. Q., and Castro,  P. M. S. T., 1997, “Linear Elastic Stress Analysis of Curved Pipes Under Generalized Loads Using a Reduced Integration Finite Ring Element,” J. Strain Anal. Eng. Des., 32, pp. 47–59.
Huang,  D. W., Redekop,  D., and Xu,  B., 1997, “Natural Frequencies and Mode Shapes of Curved Pipes,” Compos. Struct., 63, pp. 465–473.
Leung,  A. Y. T., and Kwok,  T. C., 1994, “Free Vibration Analysis of a Toroidal Shell,” Thin-Walled Struct., 19, pp. 317–332.
Zhang,  F., and Redekop,  D., 1992, “Surface Loading of a Thin-walled Toroidal Shell,” Comput. Struct., 43, pp. 1019–1028.
Yamada,  G., Kobayashi,  Y., Ohta,  Y., and Yokota,  S., 1989, “Free Vibration of a Toroidal Shell with Elliptical Cross-Section,” J. Sound Vib., 135, pp. 411–425.
Galletly,  G. D., and Galletly,  D. A., 1996, “Buckling of Complex Toroidal Shell Structures,” Thin-Walled Struct., 26, pp. 195–212.
Redekop,  D., and Xu,  B., 1999, “Vibration Analysis of Toroidal Panels Using the Differential Quadrature Method,” Thin-Walled Struct., 34, pp. 217–231.
Naboulsi,  S. K., Palazotto,  A. N., and Greer,  J. M., 2000, “Static-dynamic Analyses of Toroidal Shells,” J. Aerospace Eng., 13, pp. 110–121.
Tzou,  H. S., and Wang,  D. W., 2002, “Distributed Signals of Piezoelectric Laminated Toroidal Shell Structures,” J. Sound Vib., 254, pp. 203–218.
Tzou, H. S., 1992, “Thin-layer Distributed Piezoelectric Neurons and Muscles: Electromechanics and Applications,” Precision Sensors, Actuators, and Systems, H. S. Tzou and T. Fukuda, eds., Kluwer Academic Publishers, Dordrecht/Boston/London, pp. 175–218.
Tzou, H. S., Venkayya, V. B., and Hollkamp, J. J., 1998, “Orthogonal Sensing and Control of Continua with Distributed Transducers,” Dynamics and Control of Distributed Systems, H. S. Tzou and L. A. Bergman, eds., Cambridge University Press, pp. 304–370.
Tzou,  H. S., Bao,  Y., and Zhou,  Y., 1997, “Nonlinear Piezothermoelasticity and Multi-field Actuations—Part 1: Nonlinear Anisotropic Piezothermoelastic Shell Laminates; Part 2; Control of Nonlinear Buckling and Dynamics,” ASME J. Vibr. Acoust. 119, pp. 374–389.
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Tzou,  H. S., and Tseng,  C. I., 1990, “Distributed Piezoelectric Sensor/Actuator Design for Dynamic Measurement/ Control of Distributed Parameter Systems: A Finite Element Approach,” J. Sound Vib., 138, pp. 17–34.
Tzou,  H. S., and Ye,  R., 1994, “Piezothermoelasticity and Precision Control of Piezoelectric Systems: Theory and Finite Element Analysis,” ASME J. Vibr. Acoust., 116, pp. 489–495.
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Tzou, H. S., 1993, Piezoelectric Shells (Distributed Sensing and Control of Continua), Kluwer Academic Publishers, Boston/Dordrecht.

Figures

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A toroidal shell panel and its coordinate system
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A laminated piezoelectric shell element
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The first three mode shapes of the toroidal shell panel (Case 1). (Note: “+” and “−” denote the convex and the concave, respectively.)
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The first four mode shapes of the toroidal shell panel (Case 2). (Note: “+” and “−” donate convex and concave, respectively.)
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Toroidal shell panel laminated with three parallel piezoelectric strips
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Toroidal shell panel laminated with diagonal piezoelectric strips
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Free displacement response of the toroidal panel
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Controlled response of the toroidal panel with parallel actuator (gain=5)
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Free displacement response of the toroidal panel
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Controlled response of the toroidal panel with diagonal actuator (gain=5)
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Inferred damping ratios at different gains of the two actuator configurations

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