Dynamic Response of a Timoshenko Beam Subjected to a Moving Loadon a Foundation with Hysteretic Damping
Bibliographic record
Abstract
For many studies concerning foundation, such as rails and pavements, the mechanism for energy dissipation within a foundation is considered only to be by viscous behaviour.It is generally considered however that dissipation of energy in soil-type foundations takes place, in the main, due to internal friction damping, known as hysteretic damping.Also quite often the simpler Euler-Bernoulli beam formulation is used, hence excluding the effects of shear rigidity and radius of gyration of the beam.In this work by the use of the Timoshenko beam formulation these effects are included as it the use of a two-parameter hysteretic damped foundation.The investigation includes when the beam experiences a moving load with constant or harmonic amplitudes.Hamilton's principle is used to formulate the two governing equations when are then transformed into two algebraic equations by uncoupling and the use of a double Fourier transform w.r.t.moving space and time.The beam deflection is obtained using inverse fast Fourier transform and the solutions obtained are compared with bot Winkler and Pasternak foundation results found in the literature.Calculations are made which investigate the effect of the spatial distribution of the loading and the effects of the beam and foundation properties on the deflected shape, the maximum displacement, critical frequency and the velocity.The results can be used to assess performance and safety aspects of railway and highway structures.
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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 | 0.001 | 0.001 |
| 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 | 0.001 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.001 | 0.000 |
| Insufficient payload (model declined to judge) | 0.004 | 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".