Abstract 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.

中文翻译：

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抖振载荷下气动弹性振荡器随机扭转颤振响应的背景/共振分解

摘要 结构的完整颤振分析需要反复分析结构在不同风速下的气动弹性响应。在谱方法中，这些分析中的每一个都基于气动弹性响应的功率谱密度的积分。由于系统极点附近函数的显着峰值，传统的积分方法难以有效地估计这些积分。在本文中，我们将背景/共振分解（通常在准稳态假设下应用）扩展到气动弹性分析，其中耦合系统的刚度和阻尼随频率变化。背景分量和谐振分量都采用比众所周知的情况更一般的形式。然而，它们仍然很简单，并因此提供对响应的直接理解。提出的公式用扭转颤振的几个例子来说明，其中临界状态对应于扭转飞驰或发散。该研究仅限于单自由度系统，但构成了多自由度系统扩展的基石，在计算效率方面，这种近似变得非常有趣。