In-plane simultaneous resonance instability behaviors of a fixed arch under a two-frequency radial uniformly distributed excitation
Bibliographic record
Abstract
This paper delves into a theoretical and numerical exploration of the in-plane simultaneous resonance instability behaviors exhibited by a fixed arch subjected to a two-frequency radial uniformly distributed excitation. An intriguing and previously overlooked phenomenon of simultaneous resonance instability in fixed arches has been identified—specifically, the coexistence of superharmonic resonance and combination subharmonic resonance. The in-plane governing equation of motion was derived using Hamilton's principle and subsequently decoupled through the application of the Galerkin method . Employing the method of multiple scales, boundary excitation frequencies at varying amplitudes were determined, establishing dynamic instability zones and distinguishing between stable and unstable regions of the arch. These findings were further validated using both the finite element method and the fourth-order Runge-Kutta technique. The investigation brought to light a fascinating phenomenon wherein the concurrent manifestation of both 2-order superharmonic resonance and 1/2-order combination subharmonic resonance occurs when the sum of two excitation frequencies approaches twice the natural frequency of the arch, with one of them being approximately half of the natural frequency.
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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 | 0.001 |
| 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".