Mathematical modelling of torsional vibrations of a truncated conical shell located in an elastic medium
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Bibliographic record
Abstract
In this article, mathematical modelling of torsional vibrations of a truncated circular conical shell located in an elastic medium is carried out. It is believed that the shell is exposed to external dynamic loads, and its material is homogeneous and isotropic. Based on the exact mathematical formulation of the problem, general equations of nonstationary torsional vibrations of a truncated conical shells have been developed, from which, in particular cases, the equations of vibration of a truncated conical rod, as well as a circular cylindrical shell and a round rod follow. The desired functions found by solving the vibrational equations are used to construct a method for computing the stress-strain state of any point in the system under investigation. As an example.
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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)
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Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
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