A TUTORIAL PRESENTATION OF ALTERNATIVE SOLUTIONS TO THE FLEXIBLE BEAM ON RIGID CART PROBLEM
Bibliographic record
Abstract
A classical planar problem in forward flexible multibody dynamics is thoroughly investigated. The system consists of a damped flexible beam cantilevered to a rigid translating cart. The problem is solved using three distinctly different conventional approaches presented in roughly the chronological order in which they have been applied to flexible dynamic systems. First, a modal superposition formulation based on Bernoulli-Euler beam theory is developed. Second, an alternative solution is developed drawing exclusively on methods for rigid body dynamics combined with a knowledge of the theoretical modal behaviour of continuous beams. Third, a formulation based on the conventional finite element method using four-degree-of-freedom planar beam elements is adapted to include the rigid body motion of the cart. The relative merits of the three formulations are discussed and numerical simulation results generated using each of the three formulations are compared with each other and with a solution from a general-purpose flexible multibody dynamics formulation that is briefly outlined. The relative accuracy and efficiency of the methods and the challenges associated with generalizing each formulation are discussed.
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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".