Nonlinear vibrational behavior of multi-body dynamical systems with bi-directional piecewise linear spring constraints
Bibliographic record
Abstract
The nonlinear vibrational behavior of multi-body dynamical systems with piecewise linear spring characteristics under harmonic excitations is investigated in this paper using the Bozzak-Newmark-LCP numerical scheme. Each body is subjected to bi-directional piecewise linear spring constraints, which are activated when the initial gaps between the body and the secondary springs are consumed. The system equations of motion are discretized in the time domain using the Bozzak relaxation scheme. At each time step, a set of governing equations in terms of displacements are obtained using the Newmark integration scheme. Two auxiliary displacement vectors, complementary to the contact force vectors, are introduced to detect the engagement of gap activated springs with a resolution of the time step size. With the aid of a simple transformation, the nonlinear vibration problem of a multiple degrees-of-freedom (d.f.) piecewise-linear dynamical system is reduced to a mathematical programming problem for which an accurate and efficient solution satisfying the piecewise linear constraints everywhere can be obtained. The numerical scheme used in this paper was first validated for a single d.f. system with two-sided gap-activated springs under base excitation using the results available in the literature. Numerical results are obtained and presented for the dynamical behavior of a two-body oscillator with two primary springs and four gap-activated secondary springs under harmonic excitations over a wide range of values of system and excitation parameters.
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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 | 0.000 |
| 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)
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".