The Behavior of the Synchronous and Asynchronous Natural Frequencies for Asymmetric Double Beams
Bibliographic record
Abstract
The effect of vibrations on asymmetric double beams is a common engineering problem in various engineering applications. In this paper, the synchronous (lower) and asynchronous (higher) natural frequencies of the asymmetric double beams are calculated using the Bernoulli-Euler method. Where the traditional methods are used to find the frequency equations at different boundary conditions, such as Pinned beam, clamped-Clamped beam, Clamped-Free beam, and Clamped-Pinned beam. The increase in the stiffness of the elastic connected layer leads to an increase in the values of the high frequencies of double beams. The greatest effect of changing the thickness of one of the upper or lower beams is for CF beams and the least effect is for CP beams. The length of the beam affects the higher and lower frequencies in high and close proportions for almost all types of beams, and the least effect is only on the higher frequencies of CF beams. The influence of the modulus elasticity change is relatively small on the lower natural frequencies of all types of beams except for CF beams, and its effect is relatively large on the higher natural frequencies of the most types of beams and comparatively less on the CF beams. The effect of varying the values of mass density is relatively small on the low natural frequencies of all types of beams except for CF beams, and its effect is comparatively large on the higher natural frequencies of all types of beams and relatively less on the CF beams.
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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".