Nonlinear Vibration of a Thin-Plate Workpiece During High Speed Milling Under 1:1 Internal Resonance Condition
Bibliographic record
Abstract
In this paper, the nonlinear vibration of a thin-plate workpiece during milling process is investigated. The thin-plate workpiece is modeling as a cantilevered thin plate. The equations of motion for the thin-plate workpiece are derived based on the Kirchhoff-plate theory and the von Karman strain-displacement relations by using the Hamilton’s principle. By applying the Galerkin’s approach, the resulting equations are reduced to a two-degree-of-freedom nonlinear system with external excitations. Considering the case of 1:1 internal resonance, the method of Asymptotic Perturbation method is utilized to obtain the averaged equations of the cantilevered thin-plate workpiece. Numerical method is used to study nonlinear dynamics of the cantilevered thin plate and get the two-dimensional phase portraits, waveforms phase, three-dimensional phase and frequency spectrum phase. The result shows that the cantilevered thin-plate workpiece exhibits the complex dynamic behavior with the increase of the amplitude of the forcing excitation.
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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 | 0.001 |
| 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".