Asymptotic approximation of flutter and buffeting response of torsional aeroelastic oscillator

Flutter design consists in the repetitive computation of the structural response for increasing wind velocities until reaching the instability of the aeroelastic system. A linear model of aerodynamic forces such as that based on Scanlan derivatives can be studied by means of equivalent frequency-dependent stiffness and damping. Therefore, the analysis in the frequency domain is suitable. In a spectral analysis, the variance of the response is the integral of the corresponding power spectral density characterized by its sharp peaks in the vicinity of the natural frequencies of the system. In this paper, we present an alternative solution to standard integration methods which extends the Background/Resonant decomposition to a single degree-of-freedom frequency dependent oscillator. The proposed method avoids the need for a dense frequency discretization, which significantly cuts the CPU load. While providing a decent accuracy, it also consists in simple closed form equations which give physical understanding. The investigation is limited to a single degree-of-freedom system but provides a significant insight into more complex models where such an approximation can become more valuable. A companion paper deals with the multi-degree-of-freedom case.