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Reduction approaches for vibration control of repetitive structures. (English) Zbl 1147.74037

Summary: We present reduction approaches for vibration control of symmetric, cyclic periodic and linking structures. The condensation of generalized coordinates, the locations of sensors and actuators, and the relation between system inputs and control forces are assumed to be set in a symmetric way, so that the control system possesses the same repetition as the structure considered. By employing proper transformations of condensed generalized coordinates and the system inputs, the vibration control of an entire system can be implemented by carrying out the control of a number of sub-structures, and thus the dimension of the control problem can be significantly reduced.

MSC:

74M05 Control, switches and devices (“smart materials”) in solid mechanics
74H45 Vibrations in dynamical problems in solid mechanics
74K99 Thin bodies, structures
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References:

[1] Evensen D A. Vibration analysis of multi-symmetric structures[J]. AIAA Journal, 1976, 14(4):446–453. · doi:10.2514/3.61383
[2] Thomas D L. Dynamics of rotational periodic structures[J]. Internat J of Numerical Methods in Engineering, 1979, 14:81–102. · Zbl 0394.73059 · doi:10.1002/nme.1620140107
[3] Cai C, Cheung Y, Chan H. Uncoupling of dynamic equations for periodic structures[J]. J of Sound and Vibration, 1990, 139(2):253–263. · doi:10.1016/0022-460X(90)90886-5
[4] Chan H, Cai C, Cheung Y. Exact Analysis of Structures with Periodicity Using U-Transformation[M]. World Scientific Publication, Hong Kong, 1998.
[5] Wang Dajun, Wang C C. Natural vibration of repetitive structures[J]. Chinese J of Mechanics, 2000, 16(2):85–95.
[6] Wang Dajun, Zhou Chunyan, Jie Rong. Free and forced vibration of repetitive structures[J]. Internat J of Solids and Structures, 2003, 40:5477–5494. · Zbl 1059.74524 · doi:10.1016/S0020-7683(03)00279-8
[7] Bryson A E, Wiesinger F A. Modeling and Control of Flexible Vehicles in Space[R]. AD-A219622, 1990.
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