Equations of Nonlinear Motion of Viscoelastic Beams
Bibliographic record
Abstract
A viscoelastic nonlinear beam with cubic nonlinearities is considered. In order to obtain the equations of nonlinear motion of the beam for large deformation vibrations, the Lagrangian dynamics and Hamilton principle is used. It is considered that the beam vibrates in two directions, one in longitudinal direction and the other in the transverse direction. Large amplitude vibrations cause the nonlinearities in inertia and geometry terms. Also, due to viscoelastic property of the beam, a nonlinear damping term is appeared in the equations of motion. Using the condition of inextensible beams, the equation of motion and boundary conditions of bending vibration of a Kelvin-Voigt viscoelastic beam has been obtained. Finally, if one considers the damping coefficient to be equal to zero in the obtained equation of motion of viscoelastic system then, an equation of motion for the elastic beam will be obtained.
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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".