Nonlinear thermoelastic damping in Euler-Bernoulli beams
Bibliographic record
Abstract
Bending-mode vibrations of Euler-Bernoulli beams create oscillating strain gradients which form across the neutral axis of the structure.Due to the thermoelastic coupling between the strain and temperature fields within an elastic material, these strain gradients engender oscillating temperature gradients.In turn, the temperature gradients lead to irreversible heat conduction and entropy generation.This mode of dissipation is referred to as thermoelastic damping.To model thermoelastic damping, the governing heat equation must first be solved.For a thermoelastic solid, this takes the form of a nonlinear, partial differential equation.While linearized thermoelastic damping models are readily available in literature, developing models to accurately solve the heat equation in its full nonlinear form remains an ongoing research effort.This thesis presents a framework to study nonlinear thermoelastic damping.A new analytical model for linear thermoelastic damping was derived, along with a nonlinear solver which follows a similar conceptual structure numerically.The nonlinear solver accounts for an intrinsic type of nonlinearity referred to as 'dissipative nonlinearity'.These linear and nonlinear models were compared to one another to study the behaviour of the nonlinear response.Chapter 5: Summarized the key results and the contributions of the thesis.Made suggestions for future works that could further advance thermoelastic damping modelling.
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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) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.000 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.001 |
| Open science | 0.001 | 0.000 |
| Research integrity | 0.001 | 0.003 |
| Insufficient payload (model declined to judge) | 0.001 | 0.002 |
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; both teacher heads agree on what is shown here.
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".