Coupled longitudinal and transverse vibration of automotive belts under longitudinal excitations using analog equation method
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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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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 | 0.001 |
| 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 it