A unified nonlinear model of piezoelectric cantilever beams with complex geometries for energy harvesting applications
Bibliographic record
Abstract
Abstract It is generally known that piezoelectric material is inherently nonlinear. This nonlinearity is more apparent at high vibration amplitudes, which are generally present in a number of energy harvesting applications such as high-power machine tools, subway vehicles, aircraft engines and rotors. The effect of nonlinearity in piezoelectric energy harvesters (PEHs) implemented for these applications needs to be assessed and well understood. The purpose of this article is to model the material nonlinearities for a piezoelectric cantilever consisting of complex geometries. The geometries modeled in this work include morphological configurations (unimorph and bimorph), tapered beam profiles, partial piezoelectric layer coverage and tip mass. Within the existing literature, several geometry-specific nonlinear models are provided for the piezoelectric cantilever which makes the study of complex designs difficult. In this work, a generalized method is developed by incorporating the transfer matrix method. The nonlinear governing equations of the piezoelectric cantilever are generalized to include higher-order nonlinear terms until n th order. The governing equations are derived by utilizing the nonlinear piezoelectric constitutive equations in the extended Hamilton’s principle and a numerical Ordinary Differential Equation solver is used to obtain the PEH output. The nonlinear model is validated using finite element model, literature and experiments conducted on a bimorph PEH sample. It is found that nonlinear response of PEH is attributed to material nonlinearity and the contribution of higher-order nonlinear terms is significant.
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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".