Geodesic
On the optimal stabilization of the orthotropic rectangular plate
Proceedings of the Yerevan State University. Physical and mathematical sciences, no. 3 (1987), pp. 37-42 
A. S. Sarkisyan; M. S. Gabrielyan; Y. G. Youssif. On the optimal stabilization of the orthotropic rectangular plate. Proceedings of the Yerevan State University. Physical and mathematical sciences, no. 3 (1987), pp. 37-42. http://geodesic.mathdoc.fr/item/UZERU_1987_3_a5/
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Voir la notice de l'article provenant de la source Math-Net.Ru

The optimal stabilization problem of the oscillations of an orthotropic rectangular plate, which is fixed at the edges by hinges has been considered. The plate becomes stable by means of supplementary control action on its upper plane. The problem has been solved by Fourier’s method, after which an infinite system of a second-order ordinary differential equations was received with separable variables. The optimal control action for each equation was formed in $L_2$ field.

[1] M. S. Gabrielyan, “O stabilizatsii mekhanicheskoi sistemy moschnosti kontinuuma”, Uch. zapiski EGU, 1975, no. 2, 49–57

[2] S. G. Lekhnitskii, Anizotropnye plastinki, Gostekhizdat, M., 1957 | MR

[3] V. S. Sarkisyan, Nekotorye zadachi matematicheskoi teorii uprugosti anizotropnogo tela, Izd-vo Erevan. un-ta, Erevan, 1976 | MR

[4] A. M. Letov, “Analiticheskoe konstruirovanie regulyatorov”, Avtomatika i telemekhanika, 21:4-6 (1960)

[5] A. N. Kolmogorov, S. V. Fomin, Elementy teorii funktsii i funktsionalnyi analiz, Nauka, M., 1976, 543 pp. | MR