The Natural Frequency of Elastic Plates with Void by Ritz-Method
Bibliographic record
Abstract
To use a new computational method for the problem of the flexural vibration of thin, isotropic rectangular plates with arbitrarily positioned voids. In this paper we use static beam functions under point load as admissible functions and Rayleigh-Ritz method for analysis of discontinuous variation of rigidity of the plates. The voids of plate are expressed continuously by using extended Dirac function, which is defined as Dirac function existing continuously in prescribed region. The governing equation for a plate with voids composed of an isotropic material is formulated without modifying the rigidity of the plates, as done in the equivalent plate analogy. The natural frequencies of simply supported and clamped plates with voids are obtained from the governing equation by this energy method. The model is able to determine the frequency of plates with voids. It is shown that numerical results all converge very fast and are in excellent agreement with other researcher’s results. The numerical results obtained from the solution method used here show good agreement with results obtain form the previous equivalent plates analogy. Key Words: Plates with voids; Static beam function
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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 | 0.001 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.000 | 0.001 |
| Open science | 0.001 | 0.000 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.002 | 0.001 |
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".