The paper proposes a method for the optimal control of the vibration of elastic systems described by the wave equation. The Fourier-series method is used. Control is exerted through the boundary conditions. Explicit solutions of problems are found
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V. R. Barsegyan, “Optimal control of the vibration of a membrane with fixed intermediate states,” Uch. Zap. Yerevan. Gos. Univ., No. 1 (188), 24–29 (1998).
A. G. Butkovsky, Control Methods for Distributed-Parameter Systems [in Russian], Nauka, Moscow (1975).
M. S. Gabrielyan and L. A. Movsisyan, ”A control problem for a moving thermoelastic strip plate,” Izv. NAN Armenii, Mekh., No. 3, 15–22 (1995).
M. S. Gabrielyan and L. A. Movsisyan, ”Optimal control of the motion of elastic systems,” Izv. NAN Armenii, Mekh., No. 6, 146–153 (1999).
L. N. Znamenskaya, Control of Elastic Vibrations [in Russian], Fizmatlit, Moscow (2004).
V. A. Il’in and E. I. Moiseev, “Optimization of a boundary control by a displacement at one end of a string with second end free during an arbitrary sufficiently large time interval”, Dokl. Math., 76, No. 3, 806–811 (2007).
L. S. Saakyan and V. R. Barsegyan, “Control of the vibrations of a membrane,” in: Interuniversity Collection of Scientific Papers [in Russian], Issue 6, Yerevan (1987), pp. 119–126.
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Translated from Prikladnaya Mekhanika, Vol. 48, No. 2, pp. 137–142, March–April 2012.
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Barsegyan, V.P., Movsisyan, L.A. Optimal control of the vibration of elastic systems described by the wave equation. Int Appl Mech 48, 234–239 (2012). https://doi.org/10.1007/s10778-012-0519-9
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DOI: https://doi.org/10.1007/s10778-012-0519-9