Dynamic response of a beam on a frequency-independent damped elastic foundation to moving load
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Bibliographic record
Abstract
The dynamic displacement response of an infinitely long beam on an elastic foundation with frequency-independent linear hysteretic damping subjected to a constant amplitude or a harmonic moving load was investigated. The advance velocity was assumed to be constant. Formulations were developed in the transformed field domain using (i) a Fourier transform in moving space for moving loads of constant amplitude, (ii) a double Fourier transform in time and moving space for moving loads of arbitrary amplitude variation or to include the transient due to the initial application of the load for moving harmonic loads, and (iii) a Fourier transform in moving space for the steady-state response to moving harmonic loads. The effects of velocity, damping, loaded length, and load frequency on the deflected shape and the maximum displacement were investigated. The critical (resonant) velocities and frequencies were obtained by analyses, and expressions to find them were suggested.Key words: beam on elastic foundation, damping, Fourier transform, frequency, harmonic load, moving load, transformed field, velocity.
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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 | 0.001 | 0.001 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.001 | 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 it