By: Payam Soltani, D. D. Ganji, I. Mehdipour, A. Farshidianfar
Abstract
Based on the rippling deformations, a nonlinear continuum elastic model is developed to analyze the transverse vibration of singlewalled carbon nanotubes (SWCNTs) embedded on a Winkler elastic foundation. The nonlinear natural frequency has been derived analytically for typical boundary conditions using the perturbation method of multi-scales. The results indicate that the nonlinear resonant frequency due to the rippling is related to the stiffness of the foundation, the boundary conditions, the excitation load-to-damping ratio, and the diameter-to-length ratio. Moreover, the rippling instability of carbon nanotubes, as a structural instability, is introduced and the influences of several effective parameters on this kind of instability are widely discussed.
Abstract:
Due to the nonlocal Euler Bernoulli elastic beam theory, the effects of rippling deformation on the bending modulus and the structural bending instability of a single-walled carbon nanotube (SWCNT) are investigated. The nonlinear vibrational model of a cantilevered SWCNT is solved using the perturbation method of multiscales. The nonlinear resonant frequency and the associated ffective bending modulus of the carbon nanotube (CNT) are derived analytically. The effects of the nonlocal parameter, the external harmonic force, and the diameter-to-length ratio on the effective bending modulus are discussed widely. Moreover, the model can predict special kind of structural instability due to the rippling deformation called rippling instability. The results show that the nonlocal theory forecasts larger values for the effective bending modulus compared with the classical beam theory, especially for the stubby CNTs. Meanwhile, the rippling instability threshold will move to the higher values of the diameter-to-length ratio based on the nonlocal beam theory comparing with the local ones.
By: I Mehdipour, Payam Soltani, D. D. Ganji, A. Farshidianfar
Link:
http://www.worldscinet.com/ijn/10/1003/S0219581X11008216.html