Coupled longitudinal and transverse vibration of automotive belts under longitudinal excitations using analog equation method
Bibliographic record
Abstract
There are many studies on vibrations of moving belts originated from automotive belt drives. These studies, however, mainly consider the nonlinear effect of the transversal vibration of the belt under transversal excitation without considering the coupling effect between the transversal and longitudinal vibrations under longitudinal excitation. In this paper, a nonlinear model is built for a standing tensioned belt periodically excited longitudinally at one end with a known amplitude and frequency and with the other end clamped, which allows for coupling between the periodic longitudinal excitation and transversal vibration. The nonlinear system is solved using the Analog Equation Method. The two coupled nonlinear hyperbolic differential equations of the system are reduced to two uncoupled linear equations pertaining to the longitudinal and transverse deformation of a substitute beam with unit longitudinal and bending stiffness, respectively. The reduced equations are under a fictitious time-dependent load distribution with the same boundary and initial conditions. The fictitious forces are established numerically from the integral expression of the oscillation solution with the requirement that the equations of motion be satisfied at discreet time intervals. It is found that the transversal vibration appears as a stable and predictable beating phenomenon due to an internal resonance from the periodic energy transfer between the longitudinal excitation and the transversal vibration, which manifests itself as a standing wave.
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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 | 0.001 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.001 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.000 | 0.001 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.000 |
| Insufficient payload (model declined to judge) | 0.002 | 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".