Efficient estimation of the high-order response statistics of a wind-excited oscillator with nonlinear velocity feedback

The point-like quasi-steady aerodynamic loading in a turbulent flow is formally expressed as a function of the squared relative velocity between the fluid and the investigated structure. The three major terms governing the low-order statistics of the response are known to be related to the average loading, the linear turbulent loading and the aerodynamic damping. The three other terms in the loading, namely the quadratic turbulence term, the parametric velocity feedback term and the squared velocity term, may significantly affect the higher order statistical cumulants of the response. These latter two sources of fluid-structure interaction are usually disregarded, by lack of efficient simulation tools, except a Monte Carlo simulation of the nonlinear equation. In this paper, we provide a formal analysis of the complete nonlinear model, including thus all six terms, but mainly focusing on the importance of the two nonlinear coupling terms of the loading. Closed form solutions of the response are derived for a second-order Volterra model of this problem, under the assumption of different timescales in the loading and in the structural behavior. Two major outcomes of the analysis are, on the one hand, that the squared structural velocity term has no influence on the cumulants of the response up to order 4 and, on the other hand, that the parametric velocity feedback acts as a reduction of the non Gaussianity of the response.