Bibliographic record
Abstract
ABSTRACT This paper presents numerical techniques for computing of the response of linear and nonlinear multi-degrees-of-freedom systems. After formulation of the equations of dynamic equilibrium, the modal superposition method is presented. Techniques for reducing coordinates are discussed. Direct numerical integration methods applied to linear systems are presented. Incremental formulation of direct numerical integration methods applicable to nonlinear systems are developed. Examples illustrating the key steps in the computation are presented. RÉSUMÉ Cet article présente certaines méthodes de calcul de la réponse dynamique des sys-tèmes discrets linéaires et non linéaires à plusieurs degrés de liberté. Après la formulation des équations d'équilibre dynamique, la méthode de superposition modale est présentée. Les techniques de réduction des coordonnées sont discutées. Les méthodes directes d'intégration numérique applicable à des systèmes linéaires sont développées. On présente une formulation incrémentale des méthodes directes d'intégration numériques applicable aux systèmes non linéaires. Des exemples illustrent les applications des différentes méthodes. KEYWORDS: Vibrationfrequenciesmode shapemodal superpositioncoordinate reductiondampingstep-by-step numerical integrationlinear systemnonlinear systemMOTS-CLÉS: Vibrationfréquencesmode de vibrationsuperposition modaleréduction de coor-donnéesamortissementintégration numériquesystème linéairesystème non linéaire
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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 | 0.005 | 0.011 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.000 |
| Bibliometrics | 0.001 | 0.005 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.001 | 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 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".