HIGHER-ORDER ENERGY BALANCE METHOD FOR A SERIES OF NONLINEAR OSCILLATORY SYSTEMS
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Bibliographic record
Abstract
The aim of this paper is to use higher-order energy balance method as a novel solution procedure for investigation the nonlinear oscillation of various systems. The method is associated with collocation method and employed for a group of nonlinear problems including pure cubic nonlinearity, fractional elastic force and duffing harmonic terms. Obtained results are evaluated by comparing with the classical balance method and also the exact solutions computed numerically. It is shown our solution procedure achieves more accurate results versus the classical solution and higher agreement are observed between the newer solutions and the exact ones for the systems. Effect of initial conditions in the nonlinear natural frequencies are carried out for a range of small and large values and it is proved the proposed method is not only simple but also more reliable for analysis of such systems.
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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 | 0.001 | 0.001 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 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)
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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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