Nonlinear stability and bifurcations of an axially moving beam in thermal environment
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Bibliographic record
Abstract
The thermo-mechanical nonlinear dynamics of an axially moving beam with coupled longitudinal and transverse displacements subjected to a distributed harmonic external force is numerically investigated. This includes a case where the system is tuned to a three-to-one internal resonance between the first two transverse modes and a case where it is not is considered. Two coupled nonlinear partial differential equations for the longitudinal and transverse motions are obtained using Hamilton’s principle and constitutive relations, as well as taking into account the thermal effects. The Galerkin method is then used to discretize these equations into a set of coupled nonlinear ordinary differential equations. Two different techniques are employed to solve the resulting equations; the pseudo-arclength continuation method and direct time integration to investigate the periodic vibrations and the global dynamics of the system, respectively. The effect of different parameters on the dynamics of the system is investigated through the frequency-response curves of the system and the bifurcation diagrams of Poincaré maps. Furthermore, time histories, phase-plane portraits, and fast Fourier transforms are presented for a few different system parameter sets. It is illustrated that the system shows a broad variety of rich dynamics, depending on system parameters and the temperature rise.
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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