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.To this end, the frequency dependence of thermoelastic damping was examined by calculating the peak value for the dissipation in both the linear and nonlinear cases.Across 16 common engineering materials, this peak occurred consistently at a normalized frequency of approximately 10, which is the operating frequency normalized by the thermal relaxation time of the beam.Furthermore, a parametric analysis of the nonlinear heat equation revealed a dimensionless number, referred to as the 'nonlinearity coefficient', related to the strength of the dissipative nonlinearity.Results showing how the dissipative nonlinearity evolves as a function of both the nonlinearity coefficient and the material properties are presented.For i Chapter 5: Summarized the key results and the contributions of the thesis.Made suggestions for future works that could further advance thermoelastic damping modelling.
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 | 0.000 |
| 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 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.001 |
| Insufficient payload (model declined to judge) | 0.005 | 0.001 |
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".