The nonlinear vibrations of Single-Walled Carbon Nanotubes are analysed. The Sanders-Koiter elastic shell theory is applied in order to obtain the elastic strain energy and kinetic energy. The carbon nanotube deformation is described in terms of longitudinal, circumferential and radial displacement fields. The theory considers geometric nonlinearities due to large amplitude of vibration. The displacement fields are expanded by means of a double series based on harmonic functions for the circumferential variable and Chebyshev polynomials for the longitudinal variable. The Rayleigh-Ritz method is applied to obtain approximate natural frequencies and mode shapes. Free boundary conditions are considered. In the nonlinear analysis, the three displacement fields are re-expanded by using approximate eigenfunctions. An energy approach based on the Lagrange equations is considered in order to obtain a set of nonlinear ordinary differential equations. The total energy distribution of the shell is studied by considering combinations of different vibration modes. The effect of the conjugate modes participation is analysed.
Nonlinear vibrations and energy distribution of carbon nanotubes / Strozzi, Matteo; Manevitch, Leonid I.; Pellicano, Francesco; Smirnov, Valeri V.; Shepelev, Denis S.. - STAMPA. - (2013), pp. 185-209.
|Data di pubblicazione:||2013|
|Titolo:||Nonlinear vibrations and energy distribution of carbon nanotubes|
|Autore/i:||Strozzi, Matteo; Manevitch, Leonid I.; Pellicano, Francesco; Smirnov, Valeri V.; Shepelev, Denis S.|
|Titolo del libro:||Problems of Nonlinear Dynamics and Condensed Matter Physics. Collection of Papers dedicated to the 75th birthday of Professor Leonid Isaakovich Manevitch|
|Editore:||Semenov Institute of Chemical Physics, Russian Academy of Sciences|
|Citazione:||Nonlinear vibrations and energy distribution of carbon nanotubes / Strozzi, Matteo; Manevitch, Leonid I.; Pellicano, Francesco; Smirnov, Valeri V.; Shepelev, Denis S.. - STAMPA. - (2013), pp. 185-209.|
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