Vibration of Cracked Composite Beams: a Dynamic Finite Element
Bibliographic record
Abstract
A Dynamic Finite Element (DFE) is developed to analyze the vibration characteristics of cracked composite beams. Stress intensity factors, corrected for geometry and material anisotropy, have been used to develop the local flexibility of a through-thickness cracked uniform laminated unidirectional unbalanced beam. By exploiting the principle of virtual work and the Dynamic Trigonometric Shape Functions (DTSF’s), developed from the exact solutions to the equations governing uncoupled flexural and torsional vibrations of the system, the element Dynamic Stiffness Matrix (DSM) is developed. By implementing the local flexibility of crack, the element matrices exhibiting both mass and stiffness properties are then assembled and the boundary conditions are applied to form the eigenproblem of the overall system. The natural frequencies and modes are then extracted using the well-known Wittrick–William (W-W) root counting algorithm. Numerical tests are conducted for a flat, solid rectangular cross-section, uniform, cantilever, laminated composite beam. Both intact and damaged scenarios (for cracks located at 20% and 50% of beam length), with various crack ratios, , and ply angles, , are investigated. Numerical results on natural frequencies and convergence tests demonstrate the higher accuracy and faster convergence of the proposed DFE and its superiority over the classical Finite Element Methods (FEM).
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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 | 0.000 | 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 | 0.000 |
| 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 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".