A Background/Resonant decomposition-based method to predict the aeroelastic behavior of 2-dof oscillators

Flutter is known as an important issue when designing flexible structures under environmental loading. The frequency-domain approach is one way to carry out this analysis under aeroelastic and buffeting forces and consists of the determination of the variance of the response for all wind speeds of the design envelope. Each variance is classically obtained by numerical integration of the response power spectral densities (PSD), using a large number of integration points to capture the sharpness of their resonant peaks. This operation is particularly resource-consuming, and considerably restricts the speed of the analysis. This paper presents an alternative semi-analytical method for integrating the PSD of a two degree-of-freedom aeroelastic model, based on the Background/Resonant decomposition of the response spectra. It focuses particularly on the integration of the covariances, that model the intermodal coupling effects in the response. The proposed method is compared to other existing Background/Resonant decomposition formulations and recovers Davenport’s approximation when neglecting all aeroelastic effects. It is illustrated with an application in the form of a parametric study, and its accuracy is compared to classical numerical methods. The errors committed on the exact nodal variances are of the order of 1%.