Stability Analysis of an Industrial Blade Accounting for a Blade-Tip/Casing Nonlinear Interface
Bibliographic record
Abstract
Abstract This paper investigates the local stability analysis of periodic solutions corresponding to the nonlinear vibration response of an industrial compressor blade, NASA rotor 37, on which are applied different types of nonlinearities. These solutions are obtained using a harmonic balance method-based approach presented in a previous paper. It accounts for unilateral contact and dry friction of the rotating blade against a rigid casing through a regularized penalty law. A Lanczos filtering technique is also employed to mitigate spurious oscillations related to the Gibbs phenomenon thus enhancing the robustness of the solver. In addition, a component mode synthesis technique is used to reduce the dimension of the numerical model. Stability assessment of the computed solutions relies on Floquet theory. It is performed through the computation of the monodromy matrix as well as Hill’s method. Both methodologies are applied and thoroughly compared as the severity of the nonlinearity is gradually increased from a cubic spring to 3D contact conditions on a deformed casing. While the presented results underline the applicability of both stability assessment methodologies for all types of nonlinearities, they also put forward the much higher computational effort required when computing the monodromy matrix. Indeed, it is shown that Hill’s method yields converged results for significantly lower values of both the number of retained harmonics and the considered number of time steps thus making it a far more efficient method when dealing with industrial models. It is also underlined that the presented results are in excellent agreement with reference solution points obtained with time domain solution methods. Specific implementation tweaks that were found to be of critical importance in order to efficiently assess the stability of computed solutions are also detailed in order to provide a comprehensive view of the challenges inherent to such numerical developments.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.000 | 0.001 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.001 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.001 | 0.000 |
| Insufficient payload (model declined to judge) | 0.002 | 0.000 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".