On the Frequency Response of an Axisymmetric Non-Flat Spinning Disk
Bibliographic record
Abstract
For rotating disks, the effect of axisymmetric runout is of interest. This study examines the frequency characteristics of thin rotating discs subjected to axisymmetric non-flatness. The equations of motion used are based on Von Karman’s plate theory. First, the eigenfunctions of the stationary disk problem corresponding to the stress function and transverse displacement are found. These eigenfunctions produce an equation that can be used in the Gelrkin’s method. The initial nonflatness is assumed to be a linear combination of the eigenfunctions of the transverse displacement of the stationary disk problem. Since the initial non-flatness is assumed to be axisymmetric, only eigenfunctions with no nodal diameters are considered to approximate the initial runout. It is supposed that the disk bending deflection is small compared to disk thickness, so we can ignore the second-order terms in the governing equations corresponding to transverse displacement and stress function. After simplifying and discretizing the governing equations of motion, we can obtain a set of coupled equations of motion which takes the effect of initial axisymmetric runout into account. These equations are then used to study the effect of initial runout on the frequency response of the stationary disk. It is found that the initial runout increases the frequencies of the oscillations of a stationary disk. In the next step, we study the effect of initial non-flatness on the critical speed behavior of a spinning disk.
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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".