Nonlinear vibrations and energy exchange of single-walled carbon nanotubes. Circumferential flexural modes. (27th October 2016)

• Record Type: Journal Article
• Authors: Strozzi, Matteo; Smirnov, Valeri V.; Manevitch, Leonid I.; Milani, Massimo; Pellicano, Francesco
• Is Part Of: Journal of sound and vibration. Volume 381(2016)
• Page Start: 156
• Page End: 178
• Publication Date: 2016-10-27
• Subjects: Carbon nanotubesNonlinear vibrationsEnergy localizationCircumferential flexural modes; Sound -- Periodicals; Vibration -- Periodicals; Son -- Périodiques; Vibration -- Périodiques; Sound; Vibration; Periodicals; Electronic journals; 620.205
• DOI: 10.1016/j.jsv.2016.06.013
• Languages: English
• ISSNs: 0022-460X

Abstract

Abstract: In this paper, the nonlinear vibrations and energy exchange of single-walled carbon nanotubes (SWNTs) are studied. The Sanders–Koiter theory is applied to model the nonlinear dynamics of the system in the case of finite amplitude of vibration. The SWNT deformation is described in terms of longitudinal, circumferential and radial displacement fields. Simply supported, clamped and free boundary conditions are considered. The circumferential flexural modes (CFMs) are investigated. Two different approaches based on numerical and analytical models are compared. In the numerical model, an energy method based on the Lagrange equations is used to reduce the nonlinear partial differential equations of motion to a set of nonlinear ordinary differential equations, which is solved by using the implicit Runge–Kutta numerical method. In the analytical model, a reduced form of the Sanders–Koiter theory assuming small circumferential and tangential shear deformations is used to get the nonlinear ordinary differential equations of motion, which are solved by using the multiple scales analytical method. The transition from energy beating to energy localization in the nonlinear field is studied. The effect of the aspect ratio on the analytical and numerical values of the nonlinear energy localization threshold for different boundary conditions is investigated. Graphical abstract: Time evolution of the total energy distribution along the axis of a simply supported SWNT Highlights: The nonlinear vibrations and energy exchange along the SWNT axis are studied. The Sanders–Koiter theory is applied to model the nonlinear dynamics of the system. Two different approaches based on numerical and analytical models are proposed. The nonlinear transition from energy beating to energy localization is considered. The effect of the aspect ratio on the energy localization threshold is investigated.