Nonlinear Normal Modes and the Dahl Friction Model Parameter Identification
Bibliographic record
Abstract
Fretting wear of steam generator tubes due to vibration induced by fluid flow remains a serious problem in the nuclear industry. Azizian and Mureithi [1] have recently developed a hybrid friction model to simulate the friction behavior of tube-support interaction. However, identification of the model parameters remains unresolved. To identify the parameters of the friction model, the following quantities are required: contact forces (tangential force (friction) and normal force (impact)), the slip velocity and displacement in the contact region. Direct measurement of these quantities by using a steam generator tube interacting with its supports is difficult. To simplify the problem, a beam, clamped at one end and simply supported with consideration of friction effect at the other is used. The beam acts as a mechanical amplifier of the friction effects at the microscopic level. Using this simple setup, the contact forces, the sliding velocity and the displacement can be indirectly obtained from the beam’s vibration response measurements. A new method based on nonlinear modal analysis was developed to calculate the contact forces. This method is based on the modal superposition principle and Fourier series expansion. The nonlinear normal modes (NNMs) and the generalized coordinates (GCs) have been identified experimentally as functions of the excitation level, the frequency, the preload in the contact area, with and without lubrication. Three hypotheses and related analyses to identify the NNMs and GCs were tested; the analysis based on the harmonic balance method gives the best results for reconstructing the accelerometer signals with an error less than 2% for all excitation levels compared to more than 2% for other methods. The successful signal reconstruction makes it possible to accurately identify the parameters of the Dahl friction model. This is also the first step to identify the parameters of the hybrid friction model.
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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".