Fully coupled forced response analysis of nonlinear turbine blade vibrations in the frequency domain

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 partial 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 under-/overestimation of the resonant vibration level by the influence-coefficient-based state-of-the-art methods (which rely on this linearity assumption).