Prediction of mode-splitting phenomenon in rings deviated fromaxisymmetric
Bibliographic record
Abstract
Abstract: When a structure deviates from axisymmetric conditions for any reason, the system behaviour can be qualitatively different from that of the idealized representation. Classical approaches analyze the vibration of systems with simple geometries having homogenous material and symmetrical boundary conditions. In the presence of any perturbations in a system, the harmonic mode shapes can be contaminated by additional wavenumbers as the modes split. In this work, one of the most straightforward axisymmetric structures, namely, a ring that exhibits motion in radial and tangential directions, is investigated. The studied ring is mounted into its frame at different points with different types of supports. An analytical method is used in this research that allows one to obtain the system's natural frequencies and mode shapes when this ring is non-axisymmetric due to a nonuniformity in the boundary conditions of the ring. The deviation from the axisymmetric can cause a significant change in the system’s natural frequencies and the corresponding mode shapes. This change is crucial for cases with repeated natural frequencies and degenerated modes. For the studied cases in this work, results show that for an axisymmetrical ring, the contamination of the split modes occurs at wavenumbers far from the base modes, however, for rings with non-uniform or anti-symmetrical boundary conditions, a significant distortion occurs in the contaminant modes lower than the base natural frequencies. An algebraic relationship between the nodal diameter and the contamination wavenumber is discussed in this work, and the corresponding diagrammatic schematics for different cases are plotted. The results for different scenarios are presented and individually validated with the help of Abaqus software.
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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 | 0.001 | 0.001 |
| 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".