For the first time, a fully-coupled Harmonic Balance method is developed for the forced response of turbomachinery blades. The method is applied to a state-of-the-art model of a turbine bladed disk with interlocked shrouds subjected to wake-induced loading. The recurrent opening and closing of the pre-loaded shroud contact causes a softening effect, leading to turning points in the amplitude-frequency curve near resonance. Therefore, the coupled solver is embedded into a numerical path continuation framework. Two variants are developed: the coupled continuation of the solution path, and the coupled re-iteration of selected solution points. While the re-iteration variant is slightly more costly per solution point, it has the important advantage that it can be run completely in parallel, which substantially reduces the wall clock time. It is shown that wake- and vibration-induced flow fields do not linearly superimpose, leading to a severe underestimation of the resonant vibration level by the influence-coefficient-based state-of-the-art methods (which rely on this linearity assumption).

翻译：首次提出了用于涡轮机械叶片受迫响应的全耦合谐波平衡法。该方法应用于一个具有互锁叶冠并承受尾流激励的先进涡轮叶片盘模型。预载荷叶冠接触的反复开合导致软化效应，进而在共振附近的幅频曲线上产生转折点。因此，该耦合求解器被嵌入数值路径延续框架中。发展了两种变体：解路径的耦合延续与选定解点的耦合迭代。虽然每次解点的迭代变体计算成本略高，但其关键优势在于可完全并行运行，从而显著缩短实际计算时间。研究表明，尾流诱导与振动诱导流场并非线性叠加，这导致基于影响系数的现有方法（依赖线性叠加假设）严重低估了共振振动水平。