Two-dimensional stick-slip motion of Coulomb friction oscillators
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Bibliographic record
Abstract
Two-dimensional stick-slip motion of an oscillator subjected to dry friction is investigated in this paper. The equations of motion of the non-smooth system are discretized in the time domain by means of the implicit Bozzak-Newmark scheme. The system state equations in a time step are written in the incremental displacements to model the frictional constraints in accordance with Coulomb’s law. With the help of a coordinate transformation and introduction of paired non-negative and complementary variables, the non-smooth vibration problem is reduced to a mathematical programming problem for which a numerical solution can be obtained. Numerical results for a single body oscillator under a harmonic excitation are obtained using the proposed method and compared with those in the literature; excellent agreement is achieved. The proposed method is then applied to a general two-dimensional oscillator with stiffness and viscous coupling in addition to the frictional coupling. Experiments are conducted for free vibration of a single body vibration system subjected to two-dimensional dry friction. Good agreement between the measurements and numerical results obtained using the proposed scheme is observed.
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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 | 0.003 | 0.002 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.000 |
| Bibliometrics | 0.001 | 0.002 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.001 |
| Open science | 0.001 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 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 it