Vibration Analysis of Doubly Coupled Cracked Composite Beams: an Exact Dynamic Stiffness Matrix
Bibliographic record
Abstract
A Dynamic Stiffness Matrix (DSM) is developed to analyze the free vibration characteristics of doubly coupled, cracked, laminated, unidirectional, unbalanced composite beams. Based on the closed form solution of the governing differential equations, an ‘exact’ DSM formulation for bending-torsion vibration of an intact composite beam is first presented. Both material and geometric/structural couplings are taken into account. Stress intensity factors, corrected for geometry and material anisotropy, are used to develop the local flexibility of a through-thickness cracked uniform beam. The system is modeled using two interconnected intact beams and the crack is modeled by implementing its local flexibility. The intact elements’ DSMs exhibiting both mass and stiffness properties are then assembled and the boundary conditions are applied to form the nonlinear eigenproblem of the overall system. The natural frequencies and modes are extracted using the well-known Wittrick–William (W-W) root counting algorithm. Numerical tests are conducted for a long, slender, flat, uniform, cantilever, laminated composite beam of solid rectangular cross-section, exhibiting material couplings. Both intact and damaged scenarios for a ply angle, η=30°, the crack located at 30% of the span, and the crack ratio of α=0.3, are investigated. Numerical results on natural frequencies and modes are in excellent agreement with the literature.
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How this classification was reachedexpand
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 | 0.001 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.000 |
| Bibliometrics | 0.001 | 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 | 0.001 |
| 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 itClassification
machine, unvalidatedMachine predicted; a candidate call from one teacher head, 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".