Dynamic Stability of Fluttered Systems Subjected to Parametric Random Excitations

Abstract

A general solution for dynamic stability of the fluttered mode of damped, fluttered systems subjected to parametric random excitations is presented in this paper. First, the system equations are pairwisely uncoupled by a modal analysis based on normal modes of the system at the onset of fluttering. The stochastic averaging method is then applied to obtain Ito's equation governing the amplitude of the fluttered mode. Finally, the Lyapunov exponent of the fluttered mode is derived, from which the criterion for asymptotic sample stability of the mode is determined. A cantilevered beam acted upon by a static follower force and a white noise parametric excitation at the free end, and a skew panel subjected to an aerodynamic force in the chordwise direction and a white noise excitation in the spanwise direction are demonstrated as examples. Numerical results show that, although the static follower force or the aerodynamic force exceeds the flutter load, the fluttered mode of the beam or the panel may remain stable in the sense of asymptotic sample stability due to the presence of the white noise excitation.

Keywords

Asymptotic sample stability fluttered system parametric random vibration stochastic averaging method

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References

Bolotin, V. V. , 1963, Nonconservative Problems of the Theory of Elastic Stability, Pergamon Press, New York.

Dowell, E. H. , 1975, Aeroelasticity of Plates and Shells, Noordhoff, Leiden, The Netherlands.

Fu, F. C. L. and Nemat-Nasser, S. , 1975, “Response and stability of linear dynamic systems with many degrees of freedom subjected to nonconservative and harmonic forces,” Journal of Applied Mechanics 42, 458-463.

Herrmann, G. , 1967, “Stability of equilibrium of elastic systems subjected to nonconservative forces,” Applied Mechanics Reviews 20, 103-108.

Huseyin, K. , 1978, Vibrations and Stability of Multiple Parameter Systems, Sijthoff & Noordhoff, Alphen aan den Rijn, The Netherlands.

Leipholz, H. , 1980, Stability of Elastic Systems, Sijthoff & Noordhoff, Alphen aan den Rijn, The Netherlands.

Nemat-Nasser, S. , 1970, “Thermoelastic stability under general loads,” Applied Mechanics Reviews 23, 615-624.

Li, Q. C. and Lin, Y. K. , 1995, “New stochastic theory for bridge stability in turbulent flow. II,” Journal of Engineering Mechanics 121, 102-116.

Lin, Y. K. and Cai, G. Q. , 1995, Probabilistic Structural Dynamics, McGraw-Hill, New York.

10.

Sri Namachchivaya, N. and Lin, Y. K. , 1988, “Application of stochastic averaging for nonlinear dynamic systems with high damping,” Probabilistic Engineering Mechanics 3, 159-167.

11.

Srinivasan, R. S. and Babu, B. J. C. , 1985, “Flutter analysis of cantilevered quadrilateral plates,” Journal of Sound and Vibration 98, 45-53.

12.

Young, T. H. and Chen, F. Y. , 1994, “Stability of skew plates subjected to aerodynamic and in-plane forces,” Journal of Sound and Vibration 171, 603-615.

13.

Young, T. H. and Chen, F. Y. , 1993, “Stability of fluttered panels subjected to in-plane harmonic forces,” AIAA Journal 31, 1667-1673.

14.

Ziegler, H. , 1977, Principles of Structural Stability, Birkhauser Verlag Basel, Stuttgart.

15.

Zienkiewicz, O. C. , 1977, The Finite Element Method, McGraw-Hill (UK), Maidenhead.