Geodesic
Nonlinear panel flutter. Bolotin's problem in the presence of viscous friction
Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Proceedings of the All-Russian Scientific Conference «Differential Equations and Their Applications» dedicated to the 85th anniversary of Professor M. T. Terekhin. Ryazan State University named for S. A. Yesenin, Ryazan, May 17-18, 2019. Part 2, Tome 186 (2020), pp. 45-51.

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In this paper, we consider a nonlinear boundary-value problem proposed as the simplest model for describing oscillations in a gas flow. We analyze the stability of the zero equilibrium state and find a critical value of the velocity of the incoming gas flow. Exact solutions of the problem are found in the form of time-periodic functions and their stability is examined. All the results are obtained analytically based on the qualitative theory of infinite-dimensional dynamical systems.
Keywords: nonlinear boundary-value problem, theory of aeroelasticity, stability, periodic solution, panel flutter. 
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A. S. Zapov. Nonlinear panel flutter. Bolotin's problem in the presence of viscous friction. Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Proceedings of the All-Russian Scientific Conference «Differential Equations and Their Applications» dedicated to the 85th anniversary of Professor M. T. Terekhin. Ryazan State University named for S. A. Yesenin, Ryazan, May 17-18, 2019. Part 2, Tome 186 (2020), pp. 45-51. http://geodesic.mathdoc.fr/item/INTO_2020_186_a5/

[1] Bolotin V. V., Nekonservativnye zadachi teorii uprugoi ustoichivosti, Nauka, M., 1961

[2] Zapov A. S., “Ob odnoi matematicheskoi modeli v teorii uprugoi ustoichivosti”, Vestn. Udmurt. un-ta. Mat. Mekh. Komp. nauki., 1:29 (2019), 29–39 | MR | Zbl

[3] Kulikov A. N., “Attraktory odnoi nelineinoi kraevoi zadachi, vstrechayuscheisya v teorii aerouprugosti”, Differ. uravn., 3:37 (2001), 397–401 | Zbl

[4] Kulikov A. N., “Bifurkatsiya avtokolebanii plastinki pri malom dempfirovanii v sverkhzvukovom potoke gaza”, Prikl. mat. mekh., 2:73 (2009), 271–281 | Zbl

[5] Kulikov A. N., “O vozmozhnosti realizatsii stsenariya Landau—Khopfa perekhoda k turbulentnosti v dvukh zadachakh teorii uprugoi ustoichivosti”, Differ. uravn., 1:47 (2011), 296–298

[6] Kulikov A. N., “O realizatsii stsenariya Landau—Khopfa perekhoda k turbulentnosti v nekotorykh zadachakh teorii uprugoi ustoichivosti”, Differ. uravn., 9:48 (2012), 1278–1291 | Zbl

[7] Kulikov A. N., Nekotorye bifurkatsionnye zadachi teorii uprugoi ustoichivosti i matematicheskoi fiziki, Dissertatsiya na soiskanie uch. step. dokt. fiz.-mat. nauk, N. Novgorod, 2018

[8] Tompson Dzh. M. T., Neustoichivosti i katastrofy v nauke i tekhnike, Mir, M., 1985 | MR

[9] Yakubov S. Ya., “Razreshimost zadachi Koshi dlya abstraktnykh kvazilineinykh giperbolicheskikh uravnenii vtorogo poryadka i ikh prilozheniya”, Tr. Mosk. mat. o-va., 23 (1970), 37–60 | Zbl

[10] Paidoussis M. P., Issid N. T., “Dynamic stability of pipes conveying fluid”, J. Sound Vibr., 3:33 (1974), 267–294 | DOI