A new approach based on the solution of a singular integral equation to analyzing the aeroelastic oscillations of thin plates is proposed. The velocity circulation is expanded into a series in the generalized coordinates of oscillations of the plate. This allows using a system with a finite number of degrees of freedom for the generalized coordinates to describe the aeroelastic oscillations. The following scenario is analyzed: the motion of the plate undergoes Neimark bifurcations and transform into quasiperiodic oscillations, which, in turn, transform into chaotic oscillations
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K. V. Avramov and Yu. V. Mikhlin, Models, Methods, and Phenomena, Vol. 1 of Nonlinear Dynamics of Elastic Systems [in Russian], Inst. Komp. Issled., Moscow–Izhevsk (2010).
S. M. Belotserkovskii, Thin Lifting Surface in a Subsonic Gas Flow [in Russian], Nauka, Moscow (1965).
N. F. Vorob’ev, Aerodynamics of Lifting Surfaces in a Stationary Flow [in Russian], Nauka, Novosibirsk (1985).
E. A. Krasil’shchikova, A Thin Airfoil in a Compressible Flow [in Russian], Nauka, Moscow (1978).
K. V. Avramov and E. A. Strel’nikova, “Chaotic oscillations of plates interacting on both sides with a fluid flow,” Int. Appl. Mech., 50, No. 3, 303–309 (2014).
E. H. Dowell, H. C. Curtiss, R. H. Scanlan, and F. Sisto, A Modern Course in Aeroelasticity, Kluwer Academic Publishers, Dordrecht (1995).
C. Q. Guo and M. P. Paidoussis, “Stability of rectangular plates with free side-edges in two-dimensional inviscid channel flow,” ASME. J. Appl. Mech., No. 67, 171–176 (2000).
A. G. Haddow, A. D. S. Barr, and D. T. Mook, “Theoretical and experimental study of modal interaction in a two-degree-of-freedom structures,” J. Sound Vibr., 97, 451–473 (1984).
P. S. Koval’chuk, L. A. Kruk, and V. A. Pelykh, “Stability of differently fixed composite cylindrical shells interacting with fluid flow,” Int. Appl. Mech., 50, No. 6, 664–676 (2014).
V. D. Kubenko and P. S. Koval’chuk, “Modeling the nonlinear interaction of standing and traveling bending waves in fluid-filled cylindrical shells subject to internal resonances,” Int. Appl. Mech., 50, No. 4, 353–364 (2014).
M. T. Landahl and V. J. E. Stark, “Numerical lifting-surface theory – problems and progress,” AIAA J., No. 6, 2049–2060 (1968).
D. T. Mook and B. Dong, “Perspective: Numerical simulations of wakes and blade-vortex interaction,” ASME. J. Fluids Eng., No. 116, 5–21 (1994).
L. Morino and C.-C. Kuo, “Subsonic potential aerodynamic for complex configurations: A general theory,” AIAA J., No. 12, 191–197 (1974).
L. K. Shayo, “The stability of cantilever panels in uniform incompressible flow,” J. Sound Vibr., No. 68, 341–350 (1980).
D. Tang, E. H. Dowell, and K. C. Hall, “Limit cycle oscillations of a cantilevered wing in low subsonic flow,” AIAA J., No. 37, 364–371 (1999).
D. Tang and E. H. Dowell, “Limit cycle oscillations of two-dimensional panels in low subsonic flow,” Int. J. Non-Lin. Mech., No. 37, 1199–1209 (2002).
D. Tang, E. H. Dowell, and K. C. Hall, “Limit cycle oscillations of a cantilevered wing in low subsonic flow,” AIAA J., 37, No. 3, 364–371 (1999).
Y. Watanabe, K. Isogai, S. Suzuki, and M. Sugihara, “A theoretical study of paper flutter,” J. Fluids Struct., No. 16, 543–560 (2002).
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Translated from Prikladnaya Mekhanika, Vol. 51, No. 3, pp. 113–121, May–June 2015.
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Avramov, K.V., Strel’nikova, E.A. Saturation of Almost Periodic and Chaotic Aeroelastic Oscillations of Plates Under a Resonant Multimode Force. Int Appl Mech 51, 342–349 (2015). https://doi.org/10.1007/s10778-015-0694-6
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DOI: https://doi.org/10.1007/s10778-015-0694-6