Nonlinear transversely vibrating beams by the homotopy perturbation method with an auxiliary term
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Bibliographic record
Abstract
This paper presents the high order frequency-amplitude relationship for nonlinear transversely vibrating beams with odd and even nonlinearities using Homotopy Perturbation Method with an auxiliary term (HPMAT). The governing equations of vibrating buckled beam, beam carrying an intermediate lumped mass and quintic nonlinear beam are investigated to exhibit the reliability and ability of the proposed asymptotic approach. It is demonstrated that two terms in series expansions are sufficient to obtain a highly accurate periodic solutions. The integrity of the analytical solutions is verified by numerical results. It is clearly demonstrated that this asymptotic approach is very effective and straightforward to study the nonlinear oscillator systems include odd and even nonlinear terms.
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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 | 0.002 | 0.001 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.000 |
| Bibliometrics | 0.000 | 0.001 |
| Science and technology studies | 0.001 | 0.000 |
| Scholarly communication | 0.001 | 0.003 |
| Open science | 0.002 | 0.000 |
| Research integrity | 0.000 | 0.001 |
| Insufficient payload (model declined to judge) | 0.002 | 0.000 |
Machine scores (provisional)
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Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
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