Abstract
Thin elastic panels subjected to compression in the median plane and to supersonic gas flow are considered. An element is attached to the panel by an elastic spring and linear dashpot. The stability of the initial planar state of the panel is studied as a function of the main control parameters—such as the gas velocity and membrane force—and the parameters of the attached element. The evolution of the stability regions in the control-parameter plane is considered. Special attention is paid to compound bifurcation points and stabilization islets.
Similar content being viewed by others
References
V. V. Bolotin,Nonconservative Problems of the Theory of Elastic Stability, Pergamon, Oxford (1968).
V. V. Bolotin, “Stabilization and destabilization in elastic systems,” in:Problems of Motion Stability, Analytical Mechanics, and Motion Control [in Russian], Nauka, Novosibirsk (1979), pp. 7–17.
V. V. Bolotin, A. A. Grishko, and A. V. Petrovskii, “Influence of damping forces on the postcritical behavior of significantly nonpotential systems,”Izv. RAN. Mekh. Tverd. Tela, No. 2, 158–167 (1995).
V. V. Bolotin and B. P. Simonov, “Stability of elastic panels with added elements in a gas flow,”Izv. RAN, Mekh. Tverd. Tela, No. 2, 130–135 (1978).
V. V. Bolotin (ed.),Vibration in Engineering: A Handbook, in six volumes, Vol. 1,Oscillation of Linear Systems [in Russian], Mashinostroenie, Moscow (1978).
A. A. Grishko, Yu. A. Dubovskikh and A. V. Petrovskii, “Postcritical behavior of dissipative nonlinear systems,”Prikl. Mekh.,34, No. 6, 92–98 (1998).
A. A. Grishko, A. V. Petrovskii and V. P. Radin, “Influence of internal friction on the stability of a panel in a supersonic gas flow,”Izv. RAN, Mekh. Tverd. Tela, No. 1, 173–181 (1998).
V. V. Bolotin, “Stabilization and destabilization effects in mechanics of deformable systems,” in:Proceedings of the Sixth Canadian Congress on Applied Mechanics, Vancouver (1977), pp 1–10.
V. V. Bolotin, A. A. Grishko, A. N. Kounadis and C. Gantes, “Nonlinear panel flutter in remote postcritical domain,”Int. J. Nonlin. Mech.,33, No. 5, 753–764 (1998).
V. V. Bolotin, A. A. Grishko, A. N. Kounadis, C. Gantes and J. B. Roberts, “Influence of initial conditions on the postcritical behavior of nonlinear aeroelastic system,”J. Nonlin. Dyn., No. 15, 63–81 (1998).
V. V. Bolotin, A. V. Petrovsky and A. A. Grishko, “Secondary bifurcations and global instability of an aeroelastic nonlinear system in the divergence domain,”J. Sound Vibr.,191, No. 3, 431–451 (1996).
E. H. Dowell,Aeroelasticity of Plates and Shells, Nordhoff International, Groningen (1975).
A. N. Kounadis, “On the failure of static stability analysis of nonconservative systems in regions of divergence instability,”Int. J. Sol. Struct.,31, No. 15, 2099–2120 (1994).
W. E. Landford, “Periodic and steady-state mode interaction leading to tori,”J. Appl. Math.,37, No. 1, 22–48 (1979).
A. H. Nayfeh and B. Balachadran, “Modal interaction in dynamical and structural systems,”Appl. Mech. Rev.,42, No. 2, 175–202 (1989).
K. Huseyin, “On the stability and bifurcation phenomena associated with dynamical systems,” in: A. N. Kounadis and W. B. Krätzig (eds.),Nonlinear Stability of Structures: Theory and Computational Technique. Springer, Vienna-New York (1995), pp. 169–216.
L. N. Virgin and E. H. Dowell, “Nonlinear aeroelasticity and chaos,” in: S. N. Atluri (ed.),Computational Nonlinear Mechanics in Aerospace Engineering, AIAA, Washington (1992), pp. 531–546.
Additional information
Institute of Machine Science, Russian Academy of Sciences, Moscow, Russia. Translated from Prikladnaya Mekhanika, Vol. 35, No. 12, pp. 3–10, December, 1999.
Rights and permissions
About this article
Cite this article
Bolotin, V.V., Grishko, A.A. & Mitrichev, T.V. Stability of a thin panel with added elements in a supersonic gas flow. Int Appl Mech 35, 1191–1198 (1999). https://doi.org/10.1007/BF02682391
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF02682391