The secondary bifurcation of a noisy aeroelastic model

Abstract eng:
In this paper we study numerically the stochastic phenomenological bifurcations of a two-degree-of-freedom noisy aeroelastic system oscillating in pitch and plunge, with a cubic non-linearity in pitch. In addition to a Hopf bifurcation, the deterministic aeroelastic model has also secondary bifurcations characterized by jumps in the amplitude and the frequency of the limit cycle oscillations. Here we study the stochastic phenomenological P-bifurcations corresponding to the deterministic secondary bifurcation. The study of the phenomenological bifurcations concerns the qualitative changes of the density of the stationary distribution associated with the system, i.e of the time independent solution of the corresponding Fokker-Planck equation. Understanding the secondary bifurcation is important because some aircrafts are operated beyond the flutter speed (e.g. the F-16), and for some systems the secondary bifurcation may occur for flow velocities not very much larger than the flutter velocity. A stochastic analysis in this case is useful for validating the mathematical model and for studying the uncertainties in the limit cycle oscillations.

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