Vibration of simply supported orthotropic rectangular laminated composite cross-ply plates
Bibliographic record
Abstract
An analical solution using the propagator matrix method is developed to obtain the natural frequencies of vibration and the corresponding displacement and stress eigenvectors for simply supported, orthotropic, rectangular, laminated composite, cross- ply plates.Three approximate theories are investigated.They consist of two equivalent, single layer theories, (namely the classical laminated plate theory and first order shear deformation theory), along with a Raleigh-Ritz type approximation that uses quadratic finite elements through the thickness are investigated.Numerical results are presented for the exact propagator matrix approach as well as for the three approximate theories.Results from the novel exact solution approach agree with published results for the natural frequencies as well as the displacement and stress eigenvectors.Results for equivalent single layer theories over predict the natural frequencies.The extent of the over prediction is affected by a plate's thickness, the magnitude of the difference in the relative stiffness of the lamina, and the relative differences of the stiffness in one direction with respect to another direction.The novel solution approach that uses the propagator matrix method is computationally efficient.A new case of a zero fundamental frequency and corresponding rigid body displacement eigenvector is uncovered for an orthotropic material whose material constants, D++ and D55, re negligible.orthotropic cross-ply plate .67 4.3.4Example 4 -Multi-laminated, orthotropic cross-ply plates with equal layer thicknesses .
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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".