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  Physics Express 2011, 1: 26
  Research Article
Wave propagation characteristics in nanotubes with considering surface energies
  Yiming Fu, Jin Zhang, Liangjiao Wan  
State Key Laboratory of Advanced Technology of Design and Manufacturing for Vehicle Body Hunan University, Changsha 410082, P. R. China
  A modified continuum model of the tubular nanoscale beams is presented by incorporating surface elasticity in this paper. The classical beam theory is adopted to model the bulk, while the bulk stresses along the surfaces of the bulk substrate are required to satisfy the surface balance equations of the continuum surface elasticity. Based on the Timoshenko beam theory, the equations of motion for transverse vibration of the nanotubes are formulated, in which the effects of surface energies are taken into account. The wavenumbers and hence the phase speeds are solved from the corresponding polynomial eigenvalue problem. Beams made from silicon are chosen as examples. The numerical results show that the effects of surface energies on the angular frequency and the phase speeds of the wave motion of tubular nanobeams must be considered especially for larger wavenumbers, while this effect on the dynamic behaviors of microtubes may be neglected which indicates that the surface energies affect the results through the presence of some intrinsic length scales.
  Nanotubes; Surface energy; Wave propagation; Dispersion relation  

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