Frequency-domain unsteady lifting-line theory (ULLT) provides a means by which the aerodynamics of oscillating wings may be studied at low computational cost without neglecting the interacting effects of aspect ratio and oscillation frequency. Renewed interest in the method has drawn attention to several uncertainties however. Firstly, to what extent is ULLT practically useful for rectangular wings, despite theoretical limitations? And secondly, to what extent is a complicated wake model needed in the outer solution for good accuracy? This paper aims to answer these questions by presenting a complete ULLT based on the work of Sclavounos, along with a novel ULLT that considers only the streamwise vorticity and a Prandtl-like pseudosteady ULLT. These are compared to Euler CFD for cases of rectangular wings at multiple aspect ratios and oscillation frequencies. The results of this work establish ULLT as a low computational cost model capable of accounting for interacting finite-wing and oscillation frequency effects and identify the aspect ratio and frequency regimes where the three ULLTs are most accurate. This research paves the way towards the construction of time-domain or numerical ULLTs which may be augmented to account for nonlinearities such as flow separation.

频域非定常升力线理论 (ULLT) 提供了一种方法，可以在不忽略展弦比和振荡频率的相互作用的情况下，以较低的计算成本研究振荡机翼的空气动力学。然而，对该方法的重新关注引起了对几个不确定性的关注。首先，尽管理论上存在局限性，但 ULLT 对矩形机翼的实际有用程度如何？其次，外部解中需要在多大程度上使用复杂的尾流模型才能获得良好的精度？本文旨在通过提出基于 Sclavounos 工作的完整 ULLT 以及仅考虑流向涡度的新型 ULLT 和类 Prandtl 伪稳态 ULLT 来回答这些问题。在多个展弦比和振荡频率的矩形机翼的情况下，将这些与 Euler CFD 进行了比较。这项工作的结果将 ULLT 确立为一种低计算成本模型，能够解释相互作用的有限翼和振荡频率效应，并确定三个 ULLT 最准确的纵横比和频率范围。这项研究为构建时域或数值 ULLT 铺平了道路，这些 ULLT 可能会被增强以解决非线性问题，例如流动分离。