The harmonic balance method with arc-length continuation in blade-tip/casing contact problems

This article presents a Harmonic Balance Method-based numerical strategy to provide qualitative characterization of compressor blade’s dynamics when structural contacts occur with the surrounding casing. The mitigation Gibbs phenomenon follows two-pronged approach: (1) regularization unilateral contact law and (2) adjustment Fourier coefficients by means Lanczos filtering technique. In order validate proposed approach, it is first applied an academic cantilever rod undergoing constraints. An in-depth comparative analysis obtained results—with emphasis on displacements, forces velocities—with respect time integration-based reference underlines relevance accuracy methodology. latter then vibration industrial blade: NASA rotor 37. For given configuration, results are thoroughly compared those previously published distinct treatment algorithm. Particular attention paid demonstrate methodology for prediction forces, velocities as well stress fields within blade. Notably, evidenced that methodology, contrary strategy, able capture exact location nonlinear resonance.