Forced Vibration Analysis of Functionally Graded Beams Carrying Moving Harmonic Loads under Random Boundary Conditions
Bibliographic record
Abstract
This paper introduces forced vibration analysis of functionally graded materials (FGMs) beams subjected to moving harmonic loads in different physical and geometric states, under random boundary conditions.A mathematical model was developed based on a new refined logarithmic shear deformation theory (LSBT), used the Hamilton principle combined with the introduction of weak forms into the dynamic analysis, while including rotational inertia.The raster force is designed by the Dirac-delta function expressing moving harmonic loads.The Rayleigh-Ritz solution is used to separate system variables from equations with general boundary conditions.The fundamental frequencies of free vibration analysis are determined by solving the system of equations governing the eigenvalue problems and the modal responses of forced vibration behavior are also solved numerically using Newmark's temporal integration method.The numerical results presented make it possible to clearly appreciate the contribution of this theoretical development by examining in detail the influence of several parameters on the Dynamic Amplification Factor (DAF) of the FGMs beams.
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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 | 0.000 |
| 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) | 0.001 | 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 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".