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IssuesArchive of Issues2003-2pp.128-136

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T. V. Grishanina and F. N. Shklyarchuk, "Control of vibrations of elastic structures subject to unsteady excitations," Mech. Solids. 38 (2), 128-136 (2003)
Year 2003 Volume 38 Number 2 Pages 128-136
Title Control of vibrations of elastic structures subject to unsteady excitations
Author(s) T. V. Grishanina (Moscow)
F. N. Shklyarchuk (Moscow)
Abstract In recent years, considerable interest has been developed in adaptive elastic structures such as space-based antennas, radio-telescopes interferometers, and space stations equipped with high-precision optical and navigation systems [1]. These structures are required to maintain a prescribed shape with high degree of accuracy or to provide no vibration at certain locations, for example at the locations of optical devices. These requirements must be met for any external disturbances (excitations), which are frequently uncertain or random. In this case, the designed shape of an elastic structure and vibration damping can be provided by a control system. Active (smart) rods with controlled strains [2] can be integrated in the structure to be utilized as actuators. The length of the active rods can be adjusted by the control system on the basis of thermoelasticity or electroelasticity effects or mechanically (by means of hydraulic cylinders or screw pairs). The change in the length of such rods or the respective forces can be regarded as the control variable. Apart from space-based structures, the problem of suppression of unsteady vibrations is important also for aircraft structures [3], in particular for loads suspended under wings [4], as well as for isolation of machine operator's cabins subject to intensive vibrations and shock disturbances.

In the present paper, a mathematical model is constructed and solutions are obtained that enable one to determine control variables (forces or command signals) ensuring that a part of the elastic system would preserve the designed motion (in particular, a state of rest) under arbitrary unsteady disturbances. As an example, we have solved a quasi-static problem of control of a deformed shape of a structure.
References
1.  B. K. Wada, "Adaptive structures: an overview," Journal of Spacecraft and Rockets, Vol. 27, No. 3, pp. 330-337, 1990.
2.  F. N. Shklyarchuk and T. V. Grishanina, Dynamics of Elastic Controlled Structures [in Russian], Izd-vo MAI, Moscow, 1999.
3.  S. M. Belotserkovskii, Yu. A. Kochetkov, A. A. Krasovskii, and V. V. Novitskii, Introduction to Aeroelasticity [in Russian], Nauka, Moscow, 1980.
4.  P. V. N. Gade and D. J. Inman, "Active control of store-induced flutter in incompressible fluid," J. Aircraft, Vol. 35, No. 3, pp. 454-461, 1998.
Received 25 September 2002
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