Поширення одиночної хвилі в еластичній пластині на фундаменті Вінклера
Bibliographic record
Abstract
A new problem to find the solitary solution for interaction of elastic plate with the Winkler foundation is considered. It is assumed that the plate is characterized by elastically nonlinear properties which are described by the geometrically nonlinear deformations. It is assumed that longitudinal deformations are not taken into account, the Lagrangian corresponding to the Kirchhoff classical model of transverse bending vibrations of plate is obtained. For corresponding resolving equation a solution is found in the class of the amplitude modulated signals. By means of regularizations of formal asymptotic decompositions, the Schrödinger nonlinear equation, determining the amplitude in the first order of smallness, is obtained. We obtain the solitory solution in correspondence with considerations and results obtained by Abblowitz et al., Newel, Zakharov and Shabat. There are a lot of systems of extensive applications in various fields which include such elements. In connection with it our communication considers the problem of the interaction of an elastic plate with the Winkler foundation. A linear problem was first very clearly considered by S. P. Timoshenko as STRENGTH OF MATERIALS, vol. 1 and 2, during his work at the KPI. Since then no course, better than this one, has been developed.
Fetched live from OpenAlex and de-inverted. Abstracts are not stored in this database: the inverted indexes are 8.6 GB of the frame’s 9.3 GB of text, and the host has 13 GB free.
How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.000 | 0.001 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.002 |
| Scholarly communication | 0.002 | 0.001 |
| Open science | 0.000 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.012 | 0.004 |
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 source (direct Gemma or distilled Codex), 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".