Background/Resonant decomposition of the stochastic torsional flutter response of an aeroelastic oscillator under buffeting loads

The complete flutter analysis of a structure requires the repeated analysis of the aeroelastic response of the structure for various wind velocities. In a spectral approach, each of these analyses is based on the integration of the power spectral density of the aeroelastic response. Traditional integration methods struggle to efficiently estimate these integrals because of the marked peakedness of the function in the neighborhood of the poles of the system. In this paper, we have derived an extension of the Background/Resonant decomposition (which is commonly applied under the quasi-steady assumption), to aeroelastic analysis, where the stiffness and damping of the coupled system changes with frequency. Both the background and resonant components take a more general form than in the well known case. They remain simple, however, and offer therefore a straightforward understanding of the response. The proposed formulation is illustrated with several examples of torsional flutter, where the critical state corresponds either to torsional galloping either to divergence. The study is limited to single degree-of-freedom systems but constitute the cornerstone of an extension to multi degree-of-freedom systems, where such an approximation becomes very interesting in terms of computational efficiency.