Abstract
It is assumed in all classical studies of panel flutter that the unsteady pressure of a gas flow can be calculated according to the piston theory. But the piston theory holds only for large Mach numbers and does not cover the region 1 < M < 2. It was recently shown that, in this range of Mach numbers, there is a region of panel flutter, referred to as single-mode flutter, which differs from the “classical” (coupled) flutter. In the present paper, single-mode flutter is studied numerically for a strip-shaped periodically supported plate. The boundaries of stability are constructed, and the influence of the strip width and the distance between the supports is analyzed.
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References
A. B. Movchan, “On Vibrations of a Plate Moving in a Gas,” Prikl. Mat. Mekh. 20(2), 211–222 (1956) [J. Appl. Math. Mech. (Engl. Transl.)].
A. B. Movchan, “On Stability of a Panel Moving in a Gas,” Prikl. Mat. Mekh. 21(2), 231–243 (1957) [J. Appl. Math. Mech. (Engl. Transl.)].
A. A. Il’yushin, “Law of Plane Sections in Supersonic High-Speed Aerodynamics,” Prikl. Mat. Mekh. 20(6), 733–755 (1956) [J. Appl. Math. Mech. (Engl. Transl.)].
V. V. Bolotin, Nonconservative Problems of the Theory of Elastic Stability (Fizmatgiz, Moscow, 1961; Pergamon Press, New York, 1963).
E. I. Grigolyuk, R. E. Lamper, and K. G. Shandarov, “Flutter of Panels and Shells,” in Progress in Science and Technology. Mechanics (VINITI, Moscow, 1963), pp. 34–90 [in Russian].
J. Dugundji, “Theoretical Consideration of Panel Flutter at High Supersonic Mach Numbers,” AIAA J. 4(7), 1257–1266 (1966).
E. Y. Dowell, Aeroelasticity of Plates and Shells (Noordhoff International Publ., Leyden, 1974).
Yu. N. Novichkov, “Flutter of Plates and Shells,” in Progress in Science and Technology. Mechanics of Deformable Solids, Vol. 11 (VINITI, Moscow, 1978), pp. 67–122 [in Russian].
C. Mei, K. Abdel-Motagaly, and R. R. Chen, “Review of Nonlinear Panel Flutter at Supersonic and Hypersonic Speeds,” Appl. Mech. Rev. 10, 321–332 (1999).
S. D. Algasin and I. A. Kiiko, Flutter of Plates and Shells (Nauka, Moscow, 2006) [in Russian].
I. A. Kiiko and V. V. Pokazeev, “Vibrations and Stability of a Viscoelastic Strip Placed into a Gas Flow,” Dokl. Ross. Akad. Nauk 410(3), 342–344 (2005) [Dokl. Phys. (Engl. Transl.) 50 (3), 158–160 (2005)].
B. Duan, K. Abdel-Motagaly, X. Guo, and C. Mei, “Suppression of Supersonic Panel Flutter and Thermal Deflection Using Shape Memory Alloy,” AIAA Paper, AIAA-2003-1513 (2003).
R. C. Zhou, Z. Lai, D. Y. Xue, et al., “Suppression of Nonlinear Panel Flutter with Piezoelectric Actuation Using Finite Element Method,” AIAA J. 33(6), 1098–1105 (1995).
DunMin-De, “On the Stability of Elastic Plates in a Supersonic Stream,” Dokl. Akad. Nauk SSSR 120(4), 726–729 (1958) [Sov. Phys. Dokl. (Engl. Transl.) 3, 479–482 (1958)].
H. C. Nelson and H. J. Cunnigham, “Theoretical Investigation of Flutter of Two-Dimensional Flat Panels with One Surface Exposed to Supersonic Potential Dlow,” NACA Report No. 1280 (1956).
T. Y. Yang, “Flatter of Flat Finite Element Panels in Supersonic Potential Flow,” AIAA J. 13(11), 1502–1507 (1975) [Raketn. Tekhn. Kosmonavt. (Russ. Transl.) 13 (11), 110–117 (1975)].
O. O. Bendiksen and G. A. Davis, “Nonlinear Travelling Wave Flutter of Panels in Transonic Flow,” AIAA Paper, AIAA-95-1486 (1995).
O. O. Bendiksen and G. Seber, “Fluid-Structure Interactions with Both Structural and Fluid Nonlinearities,” J. Sound Vibr. 315(3), 664–684 (2008).
E. H. Dowell, “Aerodynamic Boundary Layer Effect on Flutter and Damping of Plates,” J. Aircraft 10(12), 734–738 (1973).
R. P. Selvam, M. R. Visbal, and S. A. Morton, “Computation of Nonlinear Viscous Panel Flutter Using a Fully-Impact Aeroelastic Solver,” AIAA Paper, AIAA-98-1844 (1998).
R. E. Gordnier and M. R. Visbal, “Computation of Three-Dimensional Nonlinear Panel Flutter,” AIAA Paper, AIAA-2001-0571 (2001).
A. Hashimoto, T. Aoyama, and Y. Nakamura, “Effect of Turbulent Boundary Layer on Panel Flutter,” AIAA J. 47(12), 2785–2791 (2009).
V. V. Vedeneev, “Flutter of a Wide Strip Plate in a Supersonic Gas Flow,” Izv. Akad. Nauk. Mekh. Zhidk. Gaza, No. 5, 155–169 (2005) [Mech. Fluids (Engl. Transl.) 40 (5), 805–817 (2005)].
A. G. Kulikovskii, “On the Stability of Homogeneous States,” Prikl. Mat. Mekh. 30(1), 148–153 (1966) [J. Appl. Math. Mech. (Engl. Transl.) 30 (1), 180–187 (1966)].
V. V. Vedeneev, “Panel Flutter at Low Supersonic Speeds,” J. Fluids Struct. 19, 79–96 (2012).
V. V. Vedeneev, “Interaction of Panel Flutter with Inviscid Boundary Layer Instability in Supersonic Flow,” J. FluidMech. 736, 216–249 (2013).
V. V. Vedeneev, “Effect of Damping on Flutter of Simply Supported and Clamped Panels at Low Supersonic Speeds,” J. Fluid Struct. 40, 366–372 (2013).
V.V. Vedeneev, S. V. Guvernyuk, A. F. Zubkov, and M. E. Kolotnikov, “Experimental Investigation of Single-Mode Panel Flutter in Supersonic Gas Flow,” Izv. Akad. Nauk. Mekh. Zhidk. Gaza, No. 2, 161–175 (2010) [Mech. Fluids (Engl. Transl.) 45 (2), 312–324 (2010)].
V. V. Vedeneev, “Nonlinear High-Frequency Flutter of a Plate,” Izv. Akad. Nauk.Mekh. Zhidk. Gaza, No. 5, 197–208 (2007) [Mech. Fluids (Engl. Transl.) 42 (5), 858–868 (2007)].
V. V. Vedeneev, “Limit Oscillatory Cycles in the Single Mode Flutter of a Plate,” Prikl. Mat. Mekh. 77(3), 355–370 (2013) [J. Appl.Math. Mech. (Engl. Transl.) 77 (3), 257–267 (2013)].
V. V. Vedeneev, “High-Frequency Flutter of a Rectangular Plate,” Izv. Akad. Nauk. Mekh. Zhidk. Gaza, No. 4, 173–181 (2006) [Mech. Fluids (Engl. Transl.) 41 (4), 641–648 (2006)].
V. V. Vedeneev, “Study of the Single-Mode Flutter of a Rectangular Plate in the Case of Variable Amplification of the Eigenmode along the Plate,” Izv. Akad. Nauk.Mekh. Zhidk. Gaza, No. 4, 163–174 (2010) [Mech. Fluids (Engl. Transl.) 45 (4), 656–666 (2010)].
A. G. Kulikovskii, “The Global Instability of Uniform Flows in Non-One-Dimensional Regions,” Prikl. Mat. Mekh. 70(2), 257–263 (2006) [J. Appl.Math. Mech. (Engl. Transl.) 70 (2), 229–234 (2006)].
J. W. Miles, The Potential Theory of Unsteady Supersonic Flow (Cambridge Univ. Press, Cambridge, 1959; Fizmatgiz, Moscow, 1963).
S. I. Soloviev, “The Finite-Element Method for Symmetric Nonlinear Eigenvalue Problems,” Zh. Vychisl. Mat. Mat. Fiz. 37(11), 1311–1318 (1997) [Comput.Math.Math. Phys. (Engl. Transl.) 37 (11), 1269–1276 (1997)].
M. A. Lavrentiev and B. V. Shabat, Method of the Theory of Functions of a Complex Variable (Nauka, Moscow, 1973) [in Russian].
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Original Russian Text © V.V. Vedeneev, S.V. Shitov, 2015, published in Izvestiya Akademii Nauk. Mekhanika Tverdogo Tela, 2015, No. 3, pp. 105–126.
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Vedeneev, V.V., Shitov, S.V. Flutter of a periodically supported elastic strip in a gas flow with a small supersonic velocity. Mech. Solids 50, 318–336 (2015). https://doi.org/10.3103/S0025654415030085
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DOI: https://doi.org/10.3103/S0025654415030085