Stability and post-critical behavior of a two-degrees of freedom aero-elastic system in a cross flow

Abstract

The linear deterministic approach of aero-elastic stability of a slender prismatic beam in a cross flow has been widely investigated in the past. Due to character of the system and regulations in practice (civil engineering, aircraft design, etc.) it can be used for determination of the lowest flow velocity of various types of instability onset. Several two degrees of freedom (TDOF) theoretical models have been worked out and experimentally validated. Nevertheless, it comes to light that a random component appearing in an external excitation can influence significantly the effective aeroelastic stability of this system. Combination of deterministic and random types of external excitation is taken into account regarding simultaneous vortex shedding and turbulence in the shear layer around the profile. Additive excitation includes deterministic (more or less harmonic) and random parts. Multiplicative excitation has a random character only and acts as a perturbation of aeroelastic and elastic parameters of the system. Some attempts for investigation of such a system have been done in the past considering noises as Gaussian white noises. Experimental measurements, however, show that these noises have character of narrow band random processes with distinctly expressed maximum in relevant spectral density. To overcome the limitation of white noises in the Fokker-Planck equation, an extended definition of correlation coefficients is used when constructing the Ito system. Then the original narrow band processes emerge in the relevant Ito system only as a couple of input process spectral density values in significant points of the system resonance curves.