Stochastic Stability of Aeroelastic Systems
by
Chong H. Koh
University of Illinois at Urbana-Champaign
Coauthors: N. Sri Namachchivaya

The stability of a flat plate under the combined influence of aerodynamic and structural forces is the subject of this investigation. The flow over the plate is assumed supersonic and modeled by piston theory aerodynamics. This paper offers a fresh approach to the investigation of aeroelastic systems by modeling the aerodynamic and structural loads as stationary random processes. Two different stochastic analyses for finding stability boundaries are presented: almost-sure stability based on the top Lyapunov exponent, utilizing the method of perturbation developed by Sri Namachchivaya and Van Roessell [1, 2], and moment stability. A variety of mathematical theories and representations are employed, such as the normal form theory and the method of stochastic averaging. It is assumed that the real noise exciting the panel is generated by passing white noise through a second order filter. The stability boundaries are then obtained in terms of the filter parameters, and also in terms of the flow velocity versus axial load for both the stochastic and deterministic cases. The destabilizing effect of noise on the system can be observed from these plots. It will be seen that the stochastic modeling of the problem yields results that are consistent with those obtained via other methods.

[1] N. Sri Namachchivaya and H.J. Van Roessel. Maximal Lyapunov exponent and rotation numbers for two coupled oscillators driven by real noise. Journal of Statistical Physics, 71(3/4):549-567, 1993.

[2] N. Sri Namachchivaya, H.J. Van Roessel, and M. M. Doyle. Moment Lyapunov exponent for two coupled oscillators driven by real noise. SIAM Journal of Applied Mathematics, 56:1400-1423, 1996.

Date received: March 6, 1998

Copyright © 1998 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # caav-13.