Dynamic Stability Analysis of Functionally Graded Timoshenko Beams with Internal Viscous Damping Distribution
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Bibliographic record
Abstract
This paper investigates the dynamic stability of functionally graded material (FGM) beams, using the Timoshenko model with internal viscous damping distribution (DIVD). It is assumed that the material properties change continuously across the thickness direction of the beam, according to the power law function for the FGM (P-FGM). The governing equations of motion were developed by the Lagrange principle. Then, the finite element method was adopted to describe unamortized natural frequencies and the damped eigenfrequencies of the dynamic system. The numerical results were compared with those available in the literature. Illustrative examples were given to show the influence of internal damping distribution, material distribution and slenderness ratio on the dynamic stability margin of FGM Timoshenko beams. The research findings provide new insights into the dynamic stability of the FGM.
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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) | 0.001 | 0.000 |
| Bibliometrics | 0.000 | 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 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 0.000 |
Machine scores (provisional)
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Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
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