Three-Dimensional Nonlinear Global Dynamics of Axially Moving Viscoelastic Beams
Bibliographic record
Abstract
The three-dimensional nonlinear global dynamics of an axially moving viscoelastic beam is investigated numerically, retaining longitudinal, transverse, and lateral displacements and inertia. The nonlinear continuous model governing the motion of the system is obtained by means of Hamilton's principle. The Galerkin scheme along with suitable eigenfunctions is employed for model reduction. Direct time-integration is conducted upon the reduced-order model yielding the time-varying generalized coordinates. From the time histories of the generalized coordinates, the bifurcation diagrams of Poincaré sections are constructed by varying either the forcing amplitude or the axial speed as the bifurcation parameter. The results for the three-dimensional viscoelastic model are compared to those of a three-dimensional elastic model in order to better understand the effect of the internal energy dissipation mechanism on the dynamical behavior of the system. The results are also presented by means of time histories, phase-plane diagrams, and fast Fourier transforms (FFT).
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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 | 0.001 |
| 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".