Coupled-mode flutter of an elastic plate in a~gas flow with a~boundary layer

V. V. Vedeneev

Trudy Matematicheskogo Instituta imeni V.A. Steklova, Modern problems of mechanics, Tome 281 (2013), pp. 149-161.

Résumé

The stability of an elastic plate in a supersonic gas flow is considered in the presence of a boundary layer formed on the surface of the plate. The problem is solved in two statements. In the first statement, the plate is of large but finite length, and a coupled-mode type of flutter is examined (the effect of the boundary layer on another, single-mode, type of flutter has been studied earlier). In the second statement, the plate is assumed to be infinite, and the character of its instability (absolute or convective) is analyzed. In both cases, the instability is determined by a branch point of the roots of the dispersion equation, and the mathematical analysis is the same. It is proved that instability in a uniform gas flow is weakened by a boundary layer but cannot be suppressed completely, while in the case of a stable plate in a uniform flow the boundary layer leads to the destabilization of the plate.

Bibliographie

[1] Carpenter P.W., Garrad A.D., “The hydrodynamic stability of flow over Kramer-type compliant surfaces. Part 1: Tollmien–Schlichting instabilities”, J. Fluid Mech., 155 (1985), 465–510 | DOI | Zbl

[2] Carpenter P.W., Garrad A.D., “The hydrodynamic stability of flow over Kramer-type compliant surfaces. Part 2: Flow-induced surface instabilities”, J. Fluid Mech., 170 (1986), 199–232 | DOI | Zbl

[3] Savenkov I.V., “Podavlenie rosta nelineinykh volnovykh paketov uprugostyu obtekaemoi poverkhnosti”, ZhVMiMF, 35:1 (1995), 95–103 | MR | Zbl

[4] O. Wiplier, U. Ehrenstein, “On the absolute instability in a boundary-layer flow with compliant coatings”, Eur. J. Mech. B: Fluids, 20:1 (2001), 127–144 | DOI

[5] Miles J., “Stability of inviscid shear flow over a flexible boundary”, J. Fluid Mech., 434 (2001), 371–378 | DOI | MR | Zbl

[6] Vedeneev V.V., “Flatter plastiny, imeyuschei formu shirokoi polosy, v sverkhzvukovom potoke gaza”, Izv. RAN. Mekhanika zhidkosti i gaza, 2005, no. 5, 155–169 | MR | Zbl

[7] Kulikovskii A.G., “Ob ustoichivosti odnorodnykh sostoyanii”, PMM, 30:1 (1966), 148–153

[8] Kulikovskii A.G., “O globalnoi neustoichivosti odnorodnykh techenii v neodnomernykh oblastyakh”, PMM, 70:2 (2006), 257–263 | MR

[9] Vedeneev V.V., “Panel flutter at low supersonic speeds”, J. Fluids Struct., 29 (2012), 79–96 | DOI

[10] Vedeneev V.V., Guvernyuk S.V., Zubkov A.F., Kolotnikov M.E., “Eksperimentalnoe issledovanie odnomodovogo panelnogo flattera v sverkhzvukovom potoke gaza”, Izv. RAN. Mekhanika zhidkosti i gaza, 2010, no. 2, 161–175

[11] Dowell E.H., “Generalized aerodynamic forces on a flexible plate undergoing transient motion in a shear flow with an application to panel flutter”, AIAA J., 9:5 (1971), 834–841 | DOI

[12] Dowell E.H., “Aerodynamic boundary layer effects on flutter and damping of plates”, J. Aircr., 10:12 (1973), 734–738 | DOI

[13] Hashimoto A., Aoyama T., Nakamura Y., “Effects of turbulent boundary layer on panel flutter”, AIAA J., 47:12 (2009), 2785–2791 | DOI

[14] Muhlstein L., Jr., Gaspers P.A., Jr., Riddle D.W., An experimental study of the influence of the turbulent boundary layer on panel flutter\, NASA TN D-4486, Ames Res. Center, NASA, Moffett Field, CA, 1968

[15] Gaspers P.A., Jr., Muhlstein L., Jr., Petroff D.N., Further results on the influence of the turbulent boundary layer on panel flutter, NASA TN D-5798, Ames Res. Center, NASA, Moffett Field, CA, 1970

[16] Vedeneev V.V., “Odnomodovyi flatter plastiny s uchetom pogranichnogo sloya”, Izv. RAN. Mekhanika zhidkosti i gaza, 2012, no. 3, 147–160 | Zbl

[17] Gaponov S.A., Maslov A.A., Razvitie vozmuschenii v szhimaemykh potokakh, Nauka, Novosibirsk, 1980 | Zbl

[18] Drazin P.G., Reid W.H., Hydrodynamic stability, Cambridge Univ. Press, Cambridge, 2004 | MR