Nonlinear Normal Modes-Related Isolated Branches of Subharmonic Solutions for Forced Response Blade-Tip/Casing Contact Problems
Bibliographic record
Abstract
Abstract This article investigates the emergence of isolated branches of solutions for blade-tip/casing structural contact configurations by means of a numerical procedure relying on Melnikov's energy principle. This study is carried out on the open fan blade model NASA rotor 67 in order to promote the reproducibility of the results. The blade is subjected to an harmonic forcing so as to initiate rubbing interactions. Contact is modeled in the frequency domain by the dynamic Lagrangian frequency-time harmonic balance method (DLFT-HBM) that accounts for vibro-impact as well as dry friction. This paper employs an isola detection procedure that was shown to give accurate results on such highly nonlinear applications. Several types of harmonic forcing are applied to the blade in order to observe subharmonic (i.e., with a fundamental frequency expressed as a fraction of the excitation frequency) isolated solutions. The existence of these solutions is shown to be related to nonlinear normal modes that feature lower periodicities than the excitation. The periodicity of the solutions is assumed to be linked to the periodicity of the nonlinear normal modes from which these solutions emerge. In some configurations, it is shown that nonlinear periodic solutions exist in the form of isolated branches while the main predicted response remains within the linear domain. This behavior is particularly detrimental since numerical strategies tackling nonlinear problems are usually not put to use when the response of the system is expected to be linear. The existence of such solutions is cross-checked by means of reference time integration simulations. Finally, an excitation of random shape is applied to show that this complex phenomenon persists for nonsimplified excitation shapes.
Fetched live from OpenAlex and de-inverted. Abstracts are not stored in this database: the inverted indexes are 8.6 GB of the frame’s 9.3 GB of text, and the host has 13 GB free.
How this classification was reachedexpand
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)
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 teacher head, 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".