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TECHNICAL PAPERS

Control of Bending Vibrations Within Subdomains of Thin Plates—Part I: Theory and Exact Solution

[+] Author and Article Information
Michael Krommer

Institute for Technical Mechanics, Johannes Kepler University Linz, Altenbergerstr. 69, A-4040 Linz, Austriae-mail: krommer@mechatronik.uni-linz.ac.at

Vasundara V. Varadan

George & Boyce Billingsley Endowed Chair and Distinguished Professor of Electrical Engineering, University of Arkansas, 3217 Bell Engineering Center, Fayetteville, AR 72701 e-mail: vvvesm@engr.uark.edu

J. Appl. Mech 72(3), 432-444 (May 06, 2005) (13 pages) doi:10.1115/1.1839185 History: Received June 11, 2004; Revised July 16, 2004; Online May 06, 2005
Copyright © 2005 by ASME
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References

Haftka,  R. T., and Adelman,  H. M., 1985, “An Analytical Investigation of Static Shape Control of Large Space Structures by Applied Temperature,” AIAA J., 23, pp. 450–457.
Irschik,  H., and Pichler,  U., 2001, “Dynamic Shape Control of Solids and Structures by Thermal Expansion Strains,” J. Therm. Stresses, 24, pp. 565–578.
Irschik,  H., 2002, “A Review on Static and Dynamic Shape Control of Structures by Piezoelectric Actuation,” Eng. Struct., 24, pp. 5–11.
Reissner,  H., 1931, “Selbstspannungen Elastischer Gebilde,” Z. Angew. Math. Mech., 11, pp. 59–70.
Nemenyi,  P., 1931, “Eigenspannungen und Eigenspannungsquellen,” Z. Angew. Math. Mech., 11, pp. 1–8.
Mura, T., 1991, Micromechanics of Defects in Solids, 2nd ed., Kluwer, Dordrecht.
Rao,  S. S., and Sunar,  M., 1994, “Piezoelectricity and Its use in Disturbance Sensing and Control of Flexible Structures: a Survey,” Appl. Mech. Rev., 47, pp. 113–123.
Gopinathan, S. V., Varadan, V. V., and Varadan, V. K., 2001, “Active Noise Control Studies Using the Rayleigh-Ritz Method,” Proceedings of IUTAM-Symposium on Smart Structures and Structronic Systems, U. Gabbert and H. S. Tzou, eds., Kluwer, Dordrecht, pp. 169–177.
Krommer, M., and Varadan, V. V., 2004, “Control of Bending Vibrations Within Sub-Domains of Thin Plates. Part II: Piezoelectric Actuation and Optimization,” ASME J. Appl. Mech, to be submitted.
Nader,  M., Gattringer,  H., Krommer,  M., and Irschik,  H., 2003, “Shape Control of Flexural Vibrations of Circular Plates by Piezoelectric Actuation,” ASME J. Vibr. Acoust., 125, pp. 88–94.
Irschik, H., Schlacher, K., and Haas, W., 1997, “Output Annihilation and Optimal H2 Control of Plate Vibrations by Piezoelectric Actuation,” Proceedings of the IUTAM-Symposium on Interactions Between Dynamics and Control in Advanced Mechanical Systems, D. H. van Campen, ed., Kluwer, Dordrecht, pp. 159–166.
Krommer, M., and Varadan, V. V., 2003, “Dynamic Shape Control of Conformal Antennas,” Proc. of SPIE’s 10th Annual International Symposium on Smart Materials and Structures, R. C. Smith, ed., Proc. SPIE Vol. 5049 (Smart Structures and Materials 2003: Modeling, Signal Processing and Control), pp. 622–630.
Nader, M., von Gassen, H. G., Krommer, M., and Irschik, H., 2003, “Piezoelectric Actuation of Thin Shells With Support Actuation,” Proc. of SPIE’s 10th Annual International Symposium on Smart Materials and Structures, R. C. Smith, ed., Proc. SPIE Vol. 5049 (Smart Structures and Materials 2003: Modeling, Signal Processing and Control), pp. 180–189.
Krommer,  M., 2003, “On the Significance of Non-Local Constitutive Relations for Composite Thin Plates Including Piezoelastic Layers With Prescribed Electric Charge,” Smart Mater. Struct., 12, pp. 318–330.
Ziegler, F., 1991, Mechanics of Solids and Fluids, Springer, New York.
Ziegler, F., and Irschik, H., 1987, “Thermal Stress Analysis Based on Maysel’s Formula,” Thermal Stresses 2, R. B. Hetnarski, ed., North-Holland, Amsterdam, pp. 120–188.
Graff, K. F., 1975, Wave Motion in Elastic Solids, Clarendon Press, Oxford.

Figures

Grahic Jump Location
Plate with subdomain to be controlled
Grahic Jump Location
Deflection of the clamped plate; ω=2π100 s−1
Grahic Jump Location
Self-moment of the clamped plate; ω=2π100 s−1
Grahic Jump Location
(a) Deflection and (b) self-moment of the clamped plate; ω=2π500 s−1
Grahic Jump Location
(a) Deflection and (b) self-moment of the clamped plate; ω=2π1000 s−1
Grahic Jump Location
Alternative domains to be controlled; (a) R≤Rsub≤Rtot, (b) R1≤Rsub1≤Rsub2≤R2
Grahic Jump Location
(a) Deflection and (b) self-moment of the clamped plate; ω=2π100 s−1
Grahic Jump Location
(a) Deflection and (b) self-moment of the clamped plate; ω=2π500 s−1
Grahic Jump Location
(a) Deflection and (b) self-moment of the clamped plate; ω=2π1000 s−1

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