The Unsteady Vortex Lattice Method has interesting capabilities for nonlinear subsonic aeroelastic analyses. This paper aims to develop an aeroelastic framework based on the UVLM that is suitable for compressible, transonic and viscous unsteady flows. To achieve these modeling capabilities, the UVLM is first extended to the nonlinear frequency domain using the harmonic balance approach. Secondly, sectional corrections are applied from a steady 2D/2.5D database of aerodynamic forces computed with high-fidelity Euler/RANS flow solvers. The angle of attack coupling scheme on the lift force is complemented by a least-square procedure also coupling the pitching moment. Finally, an approximation of the retarded time is implemented in the influence kernel of the harmonic balance formulation of the UVLM to account for unsteady compressibility. The aerodynamic model is verified against time domain high-fidelity solutions with pitching airfoils in 2D and in 3D with a pitching constant chord NACA 0012 swept wing. Thereafter, the HB/LCO approach is applied with the frequency domain UVLM to 2D and 3D aeroelastic problems and compared against high-fidelity solutions. The proposed framework is capable of capturing strong nonlinear Limit Cycle Oscillation behaviors at high Mach numbers, as well as the flutter boundary for a wide range of Mach numbers while maintaining a low computational cost. As a result, the proposed framework could be of interest for preliminary design and Multi-Disciplinary Design (MDO) optimizations in the context of subsonic and transonic aircraft design.

Unsteady Vortex Lattice Method 具有用于非线性亚音速气动弹性分析的有趣功能。本文旨在开发一种基于 UVLM 的气动弹性框架，适用于可压缩、跨音速和粘性非定常流动。为了实现这些建模功能，首先使用谐波平衡方法将 UVLM 扩展到非线性频域。其次，从使用高保真 Euler/RANS 流求解器计算出的空气动力的稳定 2D/2.5D 数据库中应用截面修正。升力的攻角耦合方案由最小二乘程序补充，也耦合俯仰力矩。最后，在 UVLM 的谐波平衡公式的影响内核中实现了延迟时间的近似值，以解决不稳定的可压缩性。空气动力学模型针对具有 2D 俯仰翼型和具有俯仰恒定弦 NACA 0012 后掠翼的 3D 时域高保真解决方案进行了验证。此后，HB/LCO 方法与频域 UVLM 一起应用于 2D 和 3D 气动弹性问题，并与高保真解决方案进行比较。所提出的框架能够捕获高马赫数下的强非线性极限循环振荡行为，以及大范围马赫数的颤振边界，同时保持低计算成本。因此，在亚音速和跨音速飞机设计的背景下，拟议的框架可能对初步设计和多学科设计 (MDO) 优化感兴趣。