Asymptotic Solution for Axial Stiffness for Supports of Pipes Conveying Fluids
Bibliographic record
Abstract
Abstract Piping systems conveying fluids are frequently subjected to harmonic excitations from various sources such as unbalanced forces in turbomachinery and pulsations from reciprocating compressors and pumps, etc. These systems are typically longitudinally supported by discrete flexible steel frames placed at regular intervals to mitigate the induced axial vibrations. In order to effectively control these vibrations, it is critical to establish the minimum axial stiffness provided by pipe supports to achieve a desired fundamental natural frequency for the system. The present study proposes an asymptotic solution to determine the minimum axial stiffness of pipe supports necessary to meet a specific axial natural frequency target. Starting with the Hamilton’s principle, the governing differential equation of motion is derived for fluid-conveying pipes supported by continuous longitudinal springs. The solution is then obtained for the cases of continuous and discrete pipe supports. The predictions of the proposed solution are compared against the predictions from the commercial finite element software. The study provides a robust analytical framework for designing pipeline support systems to mitigate their longitudinal vibrations and improve the overall system stability.
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How this classification was reachedexpand
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 itClassification
machine, unvalidatedMachine predicted; a candidate call from one teacher head, 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".