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TECHNICAL PAPERS

Active Control of Periodic Structures

[+] Author and Article Information
A. Baz

Mechanical Engineering Department, University of Maryland, College Park, MD 20742

J. Vib. Acoust 123(4), 472-479 (Jun 01, 2001) (8 pages) doi:10.1115/1.1399052 History: Received July 01, 2000; Revised June 01, 2001
Copyright © 2001 by ASME
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References

Brillouin, L., 1946, Wave Propagation in Periodic Structures, 2nd ed., Dover.
Mead,  D. J., 1970, “Free Wave Propagation in Periodically Supported, Infinite Beams,” J. Sound Vib., 11, pp. 181–197.
Cremer, L., Heckel, M., and Ungar, E., 1973, Structure-Borne Sound, Springer-Verlag, New York.
Faulkner,  M., and Hong,  D., 1985, “Free Vibrations of a Mono-Coupled Periodic System,” J. Sound Vib., 99, pp. 29–42.
Mead,  D. J., 1971, “Vibration Response and Wave Propagation in Periodic Structures,” ASME J. Eng. Ind., 93, pp. 783–792.
Mead,  D. J., 1975, “Wave Propagation and Natural Modes in Periodic Systems: I. Mono-Coupled Systems,” J. Sound Vib., 40, pp. 1–18.
Mead,  D. J., and Markus,  S., 1983, “Coupled Flexural-Longitudinal Wave Motion in a Periodic Beam,” J. Sound Vib., 90, pp. 1–24.
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Sen Gupta,  G., 1970, “Natural Flexural Waves and the Normal Modes of Periodically-Supported Beams and Plates,” J. Sound Vib., 13, pp. 89–111.
Mead,  D. J., 1976, “Loss Factors and Resonant Frequencies of Periodic Damped Sandwiched Plates,” ASME J. Eng. Ind., 98, pp. 75–80.
Mead,  D. J., 1986, “A New Method of Analyzing Wave Propagation in Periodic Structures; Applications to Periodic Timoshenko Beams and Stiffened Plates,” J. Sound Vib., 114, pp. 9–27.
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Mead,  D. J., and Bardell,  N. S., 1987, “Free Vibration of a Thin Cylindrical Shell with Periodic Circumferential Stiffeners,” J. Sound Vib., 115, pp. 499–521.
Hodges,  C. H., 1982, “Confinement of Vibration by Structural Irregularity,” J. Sound Vib., 82, pp. 441–444.
Hodges,  C. H., and Woodhouse,  J., 1983, “Vibration Isolation from Irregularity in a Nearly Periodic Structure: Theory and Measurements,” J. Acoust. Soc. Am., 74, pp. 894–905.
Cai,  G., and Lin,  Y., 1990, “Localization of Wave Propagation in Disordered Periodic Structures,” AIAA J., 29, pp. 450–456.
Ruzzene,  M., and Baz,  A., 2000, “Control of Wave Propagation in Periodic Composite Rods Using Shape Memory Inserts,” ASME J. Vibr. Acoust., 122, pp. 151–159.
Ruzzene,  M., and Baz,  A., 2000, “Attenuation and Localization of Wave Propagation in Periodic Rods Using Shape Memory Inserts,” Smart Mater. Struct., 9, pp. 805–816.
Chen,  T., Ruzzene,  M., and Baz,  A., 2000, “Control of Wave Propagation in Composite Rods Using Shape Memory Inserts: Theory and Experiments,” J. Vib. Control, 6, pp. 1065–1081.
Agnes, G., 1999, “Piezoelectric Coupling of Bladed-Disk Assemblies,” Proc. Of Smart Structures and Materials Conference on Passive Damping, T. Tupper Hyde, ed., Newport Beach, CA, SPIE-Vol. 3672, pp. 94–103.
Langley,  R. S., 1994, “On the Forced Response of One-Dimensional Periodic Structures: Vibration Localization by Damping,” J. Sound Vib., 178, pp. 411–428.
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Pierre,  C., 1988, “Mode Localization and Eigenvalue Loci Veering Phenomena in Disordered Structures,” J. Sound Vib., 126, pp. 485–502.

Figures

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Typical examples of passive periodic structures
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Typical examples of active periodic structures
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An active periodic spring-mass system
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One-dimensional periodic structure
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Filtering characteristics of the passive periodic spring-mass system with rks=1 and rkc=0. (P=Pass band, S=Stop band)
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Filtering characteristics of the active periodic spring-mass system with rks=1 and rkc=2 (P=Pass band, S=Stop band)
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Filtering characteristics of the active periodic spring-mass system with rks=1 and rkc=5 (P=Pass band, S=Stop band)
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Filtering characteristics of the active periodic spring-mass system with rks=1 and rkc=−0.75 (P=Pass band, S=Stop band)
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Filtering characteristics of the active periodic spring-mass system with rks=1 and rkc=i Ω (P=Pass band, S=Stop band)
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Effect of disorder level (sigma=σ) on the localization factor (P=Pass band, S=Stop band)
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Vibration localization at frequency Ω=0.9 with disorder level sigma=2.5 (periodic –, aperiodic – )
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Vibration localization at frequency Ω=1.75 with disorder level sigma=0.25 (periodic –, aperiodic – )
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Vibration localization at frequency Ω=1.95 with disorder level sigma=0.25 (periodic –, aperiodic – )
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Boundaries of stop and pass bands

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