Variational principles for transversely vibrating multiwalled carbon nanotubes based on nonlocal Euler-Bernoulli beam model.
basic_science · Level V
Where this comes from
- Record sourced from PubMed, PMID 19344117.
- Also identified by DOI 10.1021/nl8027087.
- No licence information is recorded for this record.
- Because redistribution is not established, this page shows the abstract only. Follow the links below for the full text.
Abstract
Variational principles are derived for multiwalled carbon nanotubes undergoing vibrations. Derivations are based on the continuum modeling with the Euler-Bernoulli beam representing the nanotubes and small scale effects taken into account via the nonlocal elastic theory. Hamilton's principle for multiwalled nanotubes is given and Rayleigh's quotient for the frequencies is derived for nanotubes undergoing free vibrations. Natural and geometric boundary conditions are derived which lead to a set of coupled boundary conditions due to nonlocal effects.