Free Vibration Analysis of Curved Sandwich Beams: A Dynamic Finite Element
Bibliographic record
Abstract
The free vibration analysis of three-layered symmetric sandwich beams is studied. The governing differential equations of motion in free vibration are coupled both in axial and bending deformations. The weighted residual method is used and the resulting weak integral form of the governing equations is discretized using the Finite Element Method (FEM) formulation. The dynamic, frequency-dependent, trigonometric shape functions, derived from the solution of the uncoupled equations, are then used to develop the element matrices. The assembly of resulting Dynamic Finite Element (DFE) matrices leads to a nonlinear eigenvalue problem. A determinant search method is then used to compute the coupled natural frequencies and modes of a symmetric, thin face-layer sandwich beam. The DFE numerical results for the first four bending-axial coupled modes, obtained from a 20-element mesh, show good agreement with FEM, exact Dynamic Stiffness Matrix (DSM) method, and other results available in the literature. All the four modes are found to be dominated by bending deformation. The discussion of results is followed by some concluding remarks.
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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 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.001 |
| 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 | 0.001 |
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".