STUDY ON VIBRATION RESPONSE OF A NON-UNIFORM BEAM WITH NONLINEAR BOUNDARY CONDITION
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Bibliographic record
Abstract
Forced vibration of non-uniform beam with nonlinear boundary condition is studied in this paper by proposing an iterative model combining Adomian Decomposition Method and modal analysis. An exponentially tapered beam with a hardening nonlinearity spring boundary is simulated as a case study. The model accuracy is proved by comparing iteration results and analysis solutions with linear and weakly nonlinear boundary conditions. Sin-weep nonlinear frequency spectrum is then obtained by the proposed model. The influence of boundary nonlinearity on the vibration response of non-uniform beam is analyzed. And the effect of different excitation amplitudes on nonlinearity in the vibration response is studied. The mathematical model and numerical solutions proposed in this paper can be used to solve and analysis broad vibration problems on general non-uniform beams with different nonlinear boundary conditionsunder various excitations.
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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 | 0.000 | 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 it