Vibrations of an Axial Bar Experiencing Periodic Unilateral Contact Using the Wavelet Balance Method
Bibliographic record
Abstract
Efficiently predicting the vibratory responses of flexible structures which experience unilateral contact is becoming of high engineering importance. An example of such a system is a rotor blade within a turbine engine; small operating clearances and varying loading conditions often result in contact between the blade and the casing. The method of weighted residuals is a effective approach to simulating such behaviour as it can efficiently enforce time-periodic solutions of lightly damped, flexible structures experiencing unilateral contact. The Harmonic Balance Method (HBM) based on Fourier expansion of the sought solution is a common formulation, though it is hypothesized wavelet bases that can sparsely define nonsmooth solutions may be superior. This is investigated herein using an axially vibrating rod with unilateral contact conditions. A distributional formulation in time is introduced allowing periodic, square-integrable trial functions to approximate the second-order equations. The mixed wavelet Petrov-Galerkin solutions are found to yield consistent or better results than HBM, with similar convergence rates and seemingly more accurate contact force prediction.
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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 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.001 | 0.000 |
| Insufficient payload (model declined to judge) | 0.001 | 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".