Vibration Confinement via Optimal Eigenvector Assignment and Piezoelectric Networks

[+] Author and Article Information
J. Tang

Department of Mechanical Engineering, The University of Connecticut, Storrs, CT 06269e-mail: jtang@engr.uconn.edu

K. W. Wang

Department of Mechanical and Nuclear Engineering, The Pennsylvania State University, University Park, PA 16802e-mail: kwwang@psu.edu

J. Vib. Acoust 126(1), 27-36 (Feb 26, 2004) (10 pages) doi:10.1115/1.1597213 History: Received September 01, 2002; Revised April 01, 2003; Online February 26, 2004
Copyright © 2004 by ASME
Your Session has timed out. Please sign back in to continue.


Song, B.-K., and Jayasuriya, S., 1993, “Active Vibration Control Using Eigenvector Assignment for Mode Localization,” Proceedings of the American Control Conference, pp. 1020–1024.
Choura,  S., 1995, “Control of Flexible Structures With the Confinement of Vibrations,” ASME J. Dyn. Syst., Meas., Control, 117(2), pp. 155–164.
Shelley,  F. J., and Clark,  W. W., 2000, “Experimental Application of Feedback Control to Localize Vibration,” ASME J. Vibr. Acoust., 122(2), pp. 143–150.
Vakakis,  A. F., 1994, “Passive Spatial Confinement of Impulsive Response in Coupled Nonlinear Beams,” AIAA J., 32(9), pp. 1902–1910.
Vakakis,  A. F., Kounadis,  A. N., and Raftoyiannis,  I. G., 1999, “Use of Non-Linear Localization for Isolating Structures From Earthquake-Induced Motions,” Earthquake Eng. Struct. Dyn., 28(1), pp. 21–36.
Keane,  A. J., 1995, “Passive Vibration Control via Unusual Geometries: The Application of Genetic Algorithm Optimization to Structural Design,” J. Sound Vib., 185(3), pp. 441–453.
Allaei, D., and Tarnowski, D. J., 1997, “Enhancing the Performance of Constrained Layer Damping Confining Vibrational Energy,” Proceedings of ASME, Active/Passive Vibration Control and Nonlinear Dynamics of Structures, DE-Vol. 95/AMD-Vol. 223, pp. 31–46.
Choura,  S., and Yigit,  A. S., 1995, “Vibration Confinement in Flexible Structures by Distributed Feedback,” Comput. Struct., 54(3), pp. 531–540.
Shelley,  F. J., and Clark,  W. W., 1996, “Eigenvector Scaling for Mode Localization in Vibrating Systems,” J. Guid. Control Dyn., 19(6), pp. 1342–1348.
Moore,  B. C., 1976, “On the Flexibility Offered by State Feedback in Multi-Variable Systems Beyond Closed-Loop Eigenvalue Assignment,” IEEE Trans. Autom. Control, AC-21(5), pp. 689–692.
Andry,  A. N., Shapiro,  E. Y., and Chung,  J. C., 1983, “Eigenstructure Assignment for Linear Systems,” IEEE Trans. Aerosp. Electron. Syst., AES-19(5), pp. 711–729.
Kwon,  B.-H., and Youn,  M.-J., 1987, “Eigenvalue-Generalized Eigenvector Assignment by Output Feedback,” IEEE Trans. Autom. Control, AC-32(5), pp. 417–421.
Kim,  H.-S., and Kim,  Y., 1999, “Partial Eigenstructure Assignment Algorithm in Flight Control System Design,” IEEE Trans. Aerosp. Electron. Syst., 35(4), pp. 1403–1408.
Datta,  B. N., Elhay,  S., Ram,  Y. M., and Sarkissian,  D. R., 2000, “Partial Eigenstructure Assignment for the Quadratic Pencil,” J. Sound Vib., 230(1), pp. 101–110.
Shelley,  F. J., and Clark,  W. W., 2000, “Active Mode Localization in Distributed Parameter Systems With Consideration of Limited Actuator Placement, Part 1: Theory,” ASME J. Vibr. Acoust., 122(2), pp. 160–164.
Shelly,  F. J., and Clark,  W. W., 2000, “Active Mode Localization in Distributed Parameter Systems With Consideration of Limited Actuator Placement, Part 2: Simulations and Experiments,” ASME J. Vibr. Acoust., 122(2), pp. 165–168.
Corr,  L. R., and Clark,  W. W., 1999, “Active and Passive Vibration Confinement Using Piezoelectric Transducers and Dynamic Vibration Absorbers,” Proc. SPIE, 3668, pp. 747–758.
Agnes,  G. S., 1994, “Active/Passive Piezoelectric Vibration Suppression,” Proc. SPIE, 2193, pp. 24–34.
Kahn, S. P., and Wang, K. W., 1994, “Structural Vibration Controls via Piezoelectric Materials With Active-Passive Hybrid Networks,” Proceedings of ASME IMECE, DE75, pp. 187–194.
Tsai,  M. S., and Wang,  K. W., 1996, “Control of a Ring Structure With Multiple Active-Passive Hybrid Piezoelectric Networks,” Smart Mater. Struct., 5(5), pp. 695–703.
Tang,  J., and Wang,  K. W., 1999, “Vibration Control of Rotationally Periodic Structures Using Passive Piezoelectric Shunt Networks and Active Compensation,” ASME J. Vibr. Acoust., 121(3), pp. 379–391.
Tang,  J., Liu,  Y., and Wang,  K. W., 2000, “Semi-Active and Active-Passive Hybrid Structural Damping Treatments via Piezoelectric Materials,” Shock Vib. Dig., 32(3), pp. 189–200.
Hagood,  N. W., and von Flotow,  A., 1991, “Damping of Structural Vibrations With Piezoelectric Materials and Passive Electrical Networks,” J. Sound Vib., 146(2), pp. 243–268.
Zhang,  Q., Slater,  G. L., and Allemang,  R. J., 1990, “Suppression of Undesired Inputs of Linear Systems by Eigenspace Assignment,” J. Guid. Control Dyn., 13(2), pp. 330–336.
Cunningham, T. B., 1980, “Eigenspace Selection Procedures for Closed-Loop Response Shaping With Modal Control,” Proceedings of the American Control Conference, pp. 178–186.
Klema,  V. C., and Laub,  A. J., 1980, “The Singular Value Decomposition: Its Computation and Some Applications,” IEEE Trans. Autom. Control, AC-25(2), pp. 164–176.
Meirovitch, L., 1980, Computational Methods in Structural Dynamics, Sijthoff & Noorhoff.
Hollkamp,  J. J., 1994, “Multimodal Passive Vibration Suppression With Piezoelectric Materials and Passive Electrical Networks,” J. Intell. Mater. Syst. Struct., 5(1), pp. 49–57.
Lewis, F. L., and Syrmos, V. L., 1995, Optimal Control, 2nd ED., Wiley, New York.
Standards Committee of the IEEE Ultrasonics, Ferroelectrics, and Frequency Control Society, 1987, An American National Standard: IEEE Standard on Piezoelectricity, The Institute of Electrical and Electronics Engineers, ANSI/IEEE Std 176-1987, New York.


Grahic Jump Location
Illustrative system consisting of mechanical structure, piezoelectric shunt circuits, and active control voltage inputs. The disturbance acts on the 8-th beam, and the vibration of the first four beams needs to be suppressed.
Grahic Jump Location
Simultaneous optimization/optimal eigenvector assignment procedure for active-passive hybrid system design
Grahic Jump Location
Frequency responses of the first beam. Solid line: original structure without shunt circuits; Dashed line: mechanical structure integrated with passive shunt circuits.
Grahic Jump Location
Shaping function for used traditional eigenstructure assignment, μ=6, 3σ=2
Grahic Jump Location
Modal energy ratio ϕiac*ϕlacia*ϕia corresponding to different eigenstructure assignment approaches
Grahic Jump Location
Beam time-responses (a) first beam; (b) second beam; (c) third beam; (d) fourth beam top sub-plot: optimal eigenvector assignment, sequential approach; second sub-plot: traditional assignment method, shaping parameters μ=6, 3σ=2; third sub-plot: traditional assignment method, shaping parameters μ=8, 3σ=4; bottom sub-plot: optimal eigenvector assignment, concurrent approach
Grahic Jump Location
Energy level comparison (logarithm scale)




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