PERIODIC AND CHAOTIC RESPONSES OF AN AXIALLY ACCELERATING VISCOELASTIC BEAM UNDER TWO-FREQUENCY EXCITATIONS
Bibliographic record
Abstract
This study focuses on the steady-state periodic response and the chaotic behavior in the transverse motion of an axially moving viscoelastic tensioned beam with two-frequency excitations. The two-frequency excitations come from the external harmonic excitation and the parametric excitation from harmonic fluctuations of the moving speed. A dynamic model is established to include the finite axial support rigidity, the material derivative in the viscoelastic constitution relation, and the longitudinally varying tension due to the axial acceleration. The derived nonlinear integro-partial-differential equation of motion possesses space-dependent coefficients. Applying the differential quadrature method (DQM) and the integral quadrature method (IQM) to the equation of the transverse motion, a set of nonlinear ordinary differential equations is obtained. Based on the Runge–Kutta time discretization, the time history of the axially moving beam is numerically solved for the case of the primary resonance, the super–harmonic resonance, and the principal parametric resonance. For the first time, the nonlinear dynamics is studied under various relations between the forcing frequency and the parametric frequency, such as equal, multiple, and incommensurable relationships. The stable periodic response and its sensitivity to initial conditions are determined using the bidirectional frequency sweep. Furthermore, chaotic motions are identified using different methods including the Poincaré map, the maximum Lyapunov exponent, the fast Fourier transforms, and the initial value sensitivity. Numerical simulations reveal the characteristics of the periodic, quasiperiodic, and chaotic motion of a nonlinear axially moving beam under two-frequency excitations.
Fetched live from OpenAlex and de-inverted. Abstracts are not stored in this database: the inverted indexes are 8.6 GB of the frame’s 9.3 GB of text, and the host has 13 GB free.
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 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.001 | 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".