Nonlinear Vibration Analysis of a Beam with a Breathing Crack
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Bibliographic record
Abstract
The phenomena of sub- and super-harmonic responses make up one of the prominent nonlinear characteristics of a beam with a breathing crack. In order to fully understand the behaviors of sub- and super-harmonic resonances, it is necessary to analyze the nonlinear vibration of a beam-like structure with a breathing crack. In this study, a new stiffness model that considers the influence of the partial crack closure is proposed to model the stiffness variation of the cracked beam. Based on the finite element model of a beam with a breathing crack, the multiple-scale method is proposed to analyze the nonlinear vibration of a cracked beam subjected to harmonic excitation, and the relation between the nonlinear vibration of the cracked beam and the system parameters is obtained. An experiment is conducted to validate the analytical results. The study shows that the nonlinear responses of a beam with a breathing crack are affected by both the structural parameters and the crack parameters.
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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 | 0.001 |
| 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 it