Dynamic stability of piles with fractional damping foundation
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Bibliographic record
Abstract
This paper investigates the dynamic stability and vibration response of a slender pile embedded in soil, both theoretically and numerically. The pile is modeled as a column resting on a Winkler-type elastic foundation with fractional damping characteristics. Investigation of the pile loaded axially leads to a fractional Mathieu differential equation of motion. To analyze stability, the Bolotin method is employed to derive approximate instability boundaries. Additionally, a numerical approach based on block-pulse functions is developed to construct detailed instability diagrams, which also serve to validate the theoretical results obtained using the Bolotin method. It is found that higher order instability regions generally need higher order infinite determinants. Finally, a numerical case study is presented to explore the effects of key parameters—such as the fractional order, foundation stiffness, damping coefficient, and static and dynamic load components—on the pile’s dynamic stability. The dynamic stability of a pile subjected to a real earthquake is determined.
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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) | 0.000 | 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) | 0.000 | 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