Variational Principles for Multiwalled Carbon Nanotubes Undergoing Vibrations Based on Nonlocal Timoshenko Beam Theory

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Kucuk I., SADEK I. S., Adali S.

JOURNAL OF NANOMATERIALS, 2010 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Basım Tarihi: 2010
  • Doi Numarası: 10.1155/2010/461252
  • Dergi Adı: JOURNAL OF NANOMATERIALS
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Yıldız Teknik Üniversitesi Adresli: Hayır

Özet

Variational principles are derived for multiwalled carbon nanotubes undergoing linear vibrations using the semi-inverse method with the governing equations based on nonlocal Timoshenko beam theory which takes small scale effects and shear deformation into account. Physical models based on the nonlocal theory approximate the nanoscale phenomenon more accurately than the local theories by taking small scale phenomenon into account. Variational formulation is used to derive the natural and geometric boundary conditions which give a set of coupled boundary conditions in the case of free boundaries which become uncoupled in the case of the local theory. Hamilton's principle applicable to this case is also given.