Chaotic response of a Galerkin shell to constant load and periodic excitation
Bibliographic record
Abstract
This study intends to investigate the dynamic behaviour of a non-linear elastic shallow shell of large deflection subjected to constant boundary loading and harmonic lateral excitation. The general governing equation for the shell is established using the Galerkin Principle. Three types of dynamic equation of the shell are developed, corresponding to certain geometry and loading conditions. Melnikov functions are considered for each type. Non-linear responses of the shell to the loads are analysed theoretically. Centre points, saddle points, and homoclinic orbits are determined and analysed on the basis of the governing equations established. The critical conditions for chaos to occur are provided for the vibrations of the shell. Numerical analysis is also performed for the non-linear elastic shell. Chaotic and regular vibrations of the shell are analysed with presentations of time history plots, phase diagrams, and Poincaré maps.
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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 | 0.001 | 0.001 |
| 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".