An investigation into the free vibrations of carbon nanotubes using analytical and finite element methods
Bibliographic record
Abstract
Since their discovery, immense attention has been given to carbon nanotubes (CNTs), due to their exceptional thermal, electronic and mechanical properties and, therefore, the wide range of applications in which they are, or can be potentially, employed. Hence, it is important that all the properties of carbon nanotubes are studied extensively. This thesis studies the vibrational frequencies of double-walled and triple-walled CNTs, with and without an elastic medium surrounding them, by using Finite Element Method (FEM) and Dynamic Stiffness Matrix (DSM) formulations, considering them as Euler-Bernoulli beams coupled with van der Waals interaction forces. For FEM modelling, the linear eigenvalue problem is obtained using Galerkin weighted residual approach. The natural frequencies and mode shapes are derived from eigenvalues and eigenvectors, respectively. For DSM formulation of double-walled CNTs, a nonlinear eigenvalue problem is obtained by enforcing displacement and load end conditions to the exact solution of single equation achieved by combining the coupled governing equations. The natural frequencies are obtained using Wittrick-Williams algorithm. FEM formulation is also applied to both double and triple-walled CNTs modelled as nonlocal Euler-Bernoulli beam. The natural frequencies obtained for all the cases, are in agreement with the values provided in literature.
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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".