Vibration analysis of a cracked beam using the finite element method
Bibliographic record
Abstract
This study is motivated by the condition monitoring and fault diagnostics of structural beams used in large-scale vibrating screens for the mining industry. For the purpose of developing a reliable model-based approach, a new stiffness matrix of a three-dimensional finite element is proposed for modelling a beam with a breathing crack. Using the obtained stiffness matrix, a finite element model was derived for a cracked beam subjected to a bidirectional base excitation. With the model, a computer simulation was conducted to examine the influence of the crack depth on the natural frequencies of the beam. The numerical results show that the crack influences mainly the natural frequencies of the bending modes in the direction of the crack's growth. The simulation also investigates the responses of the beam subjected to a harmonic base excitation in two directions. The numerical results show that the responses of the cracked beam contain several superharmonic components, and the amplitude of superharmonic components increases with the increase in crack depth. Experiments are conducted to validate the proposed dynamic model using both impact testing and forced testing.
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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 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.001 | 0.000 |
| 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".