Characterizing acceleration spikes due to stiffness changes in nonlinear systems
Bibliographic record
Abstract
Abstract Recent studies have reported very large accelerations after stiffness changes in nonlinear systems, particularly self‐centering systems. Some have attributed these accelerations to numerical modelling choices and have assumed that they could be eliminated if the modelling were refined. Others have concluded that self‐centering systems generally have much larger peak accelerations than more traditional systems. This paper demonstrates that accelerations at changes in stiffness are caused by physical phenomena but may be amplified by modelling decisions. This is done by examining the response of a two‐degree‐of‐freedom system after a change in stiffness and by developing a closed‐form mathematical model to characterize this response. The equation shows that acceleration spikes should be expected near small masses and near nonlinear springs that are initially nearly rigid, particularly when those springs change from low stiffness to high stiffness while moving at a high velocity. These acceleration spikes depend on system properties that are often not known precisely, so without physical testing, analytical estimates of the accelerations that occur in nonlinear systems after stiffness changes should be treated with skepticism. Copyright © 2010 John Wiley & Sons, Ltd.
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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 | 0.002 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.001 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.001 |
| 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".