A Study on the Characteristics of a Nonlinear Oscillatory System With Dry Friction
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Bibliographic record
Abstract
Nonlinear oscillatory system involved with friction is very common in nonlinear dynamics of engineering fields. This paper is to investigate the motions a nonlinear oscillatory system with involvement of dry friction. The cases of weakly and highly nonlinearity of the system are considered. Approximate and numerical solutions for the system are developed via the author’s newly developed P-T method. As demonstrated in the present work, the properties of the weakly and highly nonlinear systems exhibit great differences, though the governing equations of the two systems employ identical system parameters. The approximate solutions developed for the system are continuous everywhere on the time range considered. Under the conditions of weakly nonlinearity, the approximate solutions developed can therefore be conveniently implemented for the purpose of an analytical studying the properties of the system with numerous system parameters and various initial conditions. Taking this advantage, the behavior of motion of the weakly nonlinear system is analyzed and compared with the corresponding solutions developed with Van der Pol’s method. It is found in the present work, the system may undergo a self-excited oscillation under certain conditions. The highly nonlinear system is a physically much involved one. Its behavior is thus much complex in comparing with that of the weakly nonlinear system. Based on the approximate solutions developed for the highly nonlinear system, recurrence relations are generated for numerical calculations. For the sake of comparison with the oscillation of the weakly nonlinear system, numerical simulations for the highly nonlinear system are performed under the same initial conditions and identical system parameters. The conditions of convergence and divergence of the weakly nonlinear system are also established for application. Behavior of the oscillatory motion of the highly nonlinear system is investigated on the basis of the corresponding numerical solutions developed.
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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 |
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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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