Nonlinear Vibration and Periodicity Analysis of Timoshenko Beams Under Harmonic Base Excitation
Bibliographic record
Abstract
Abstract The parametric response of a cantilever thick beam with a tip mass subjected to harmonic axial support motion is investigated. The governing non-linear equation of motion is derived for an arbitrary axial support motion. To formulate a simple, physically correct dynamic model for the stability and periodicity analyses, the governing equation is truncated to the first characteristic mode of vibration. Using Green’s function and Schauder’s fixed point theorem, the necessary and sufficient conditions for the existence of periodic oscillatory behavior of the beam are established. The influence of the harmonic base excitation parameters, i.e., the excitation amplitude and frequency, on the steady-state amplitude of vibration are determined. Depending on the values of the excitation amplitude and frequency in the stable and unstable regions, the solution exhibits many shapes besides the transition periodic shapes. Numerical results indicate that for a given beam under a known excitation, increasing the tip mass would usually reduce the stable periodic region. To show the effect of rotary inertia and shear deformation, the beam model is reduced to the Euler-Bernoulli and purely flexural beam theories, respectively. The results show that using purely flexural or even Euler-Bernoulli model rather than Timoshenko, would produce an incorrect periodic region.
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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 | 0.001 |
| 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 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".