The nonlinear vibrations of Single-Walled Carbon Nanotubes are analysed. The Sanders-Koiter thin shell theory is applied in order to obtain the elastic strain and kinetic energy. The carbon nanotube deformation is described in terms of axial, 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 then considered 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 is analysed.

Nonlinear vibrations and energy distribution of carbon nanotubes / Andrisano, Angelo Oreste; Manevitch, Leonid I.; Pellicano, Francesco; Strozzi, Matteo. - (2013). (Intervento presentato al convegno Settima Giornata di Studio “Ettore Funaioli” GEF 2013 tenutosi a Bologna, Italy nel July 19, 2013).

### Nonlinear vibrations and energy distribution of carbon nanotubes

#### Abstract

The nonlinear vibrations of Single-Walled Carbon Nanotubes are analysed. The Sanders-Koiter thin shell theory is applied in order to obtain the elastic strain and kinetic energy. The carbon nanotube deformation is described in terms of axial, 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 then considered 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 is analysed.
##### Scheda breve Scheda completa Scheda completa (DC)
2013
Settima Giornata di Studio “Ettore Funaioli” GEF 2013
Bologna, Italy
July 19, 2013
Andrisano, Angelo Oreste; Manevitch, Leonid I.; Pellicano, Francesco; Strozzi, Matteo
Nonlinear vibrations and energy distribution of carbon nanotubes / Andrisano, Angelo Oreste; Manevitch, Leonid I.; Pellicano, Francesco; Strozzi, Matteo. - (2013). (Intervento presentato al convegno Settima Giornata di Studio “Ettore Funaioli” GEF 2013 tenutosi a Bologna, Italy nel July 19, 2013).
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Utilizza questo identificativo per citare o creare un link a questo documento: `https://hdl.handle.net/11380/1084144`