Computation of Isolated Periodic Solutions for Forced Response Blade-Tip/Casing Contact Problems
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Bibliographic record
Abstract
Abstract This article introduces a numerical procedure dedicated to the identification of isolated branches of solutions for nonlinear mechanical systems. Here, it is applied to a fan blade subject to rubbing interactions and harmonic forcing. Both contact, which is initiated by means of the harmonic forcing, and dry friction are accounted for. The presented procedure relies on the computation of the system's nonlinear normal modes (NNM) and their analysis through the application of an energy principle derived from the Melnikov function. The dynamic Lagrangian frequency-time strategy associated with the harmonic balance method (DLFT-HBM) is used to predict the blade's dynamics response as well as to compute the autonomous nonlinear normal modes. The open industrial fan blade NASA rotor 67 is employed in order to avoid confidentiality issues and to promote the reproducibility of the presented results. Previous publications have underlined the complexity of NASA rotor 67's dynamics response as it undergoes structural contacts, thus making it an ideal benchmark blade when searching for isolated solutions. The application of the presented procedure considering a varying amplitude of the harmonic forcing allows to predict isolated branches of solutions featuring nonlinear resonances. With the use of the Melnikov energy principle, nonlinear modal interactions are shown to be responsible for the separation of branches of solutions from the main response curve. In the end, the application of the presented procedure on an industrial blade model with contact interactions demonstrates that it is both industry-ready and applicable to highly nonlinear mechanical systems.
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Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.000 | 0.000 |
| 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 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 0.000 |
Machine scores (provisional)
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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 it