Energy harvesting from a non-linear standing beam–mass system: Two- versus one-mode approximations
Bibliographic record
Abstract
We investigate the effect of including the second mode of natural vibration on the computed response of a forced non-linear gravity-loaded beam–mass structure used for non-linear piezoelectric energy harvesting. Using the method of assumed-modes and Lagrange’s equations, we develop the discretized equations of generalized coordinates of the system including the electro-mechanical equation. The equation of motion is further simplified to find the single-mode approximation. The phase-portraits, time-histories, Poincaré sections, and frequency–response curves of the system are computed. It is shown that the number of mode shapes affects the response, and it is required to include higher modes to improve the analytical–computational results. The system shows distinct behavior varying from a linear single-frequency response to a multi-frequency chaotic response. The average power across the load resistor consequently shows a noticeable variation depending on the characteristics of the overall system response.
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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".