Vibration analysis of a cantilevered trapezoidal moderately thick plate with variable thickness
Bibliographic record
Abstract
This paper presents a numerical solution for vibration analysis of cantilevered non-uniform trapezoidal thick plates.Based on the first shear deformation theory, kinetic and strain energies of the plate are derived and using Hamilton's principle, governing equations and boundary conditions are derived.A transformation of coordinates is used to convert the equations and boundary conditions from the original coordinates into a new computational coordinates.Using Differential quadrature method (DQM), natural frequencies and corresponding modes are derived numerically.Convergence and accuracy of the proposed solution are confirmed using results presented by other authors and also results obtained based on the finite element method using ANSYS software.Finally, as the case studies, two cases for variation of thickness are considered and the effects of angles, aspect ratio and thickness of the plate on the natural frequencies are studied.It is concluded that two angles of the trapezoid have opposite effect on the natural frequencies.Also, it is shown that all frequencies rise as value of thickness increases or value of the aspect ratio of the plate decreases.The most advantage of the proposed solution is its applicability for plates with variable thickness.
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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 | 0.000 |
| 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) | 0.001 | 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".