VIBRATIONS OF SERIES OF BEAMS CONNECTED BY FLEXIBLE NONLINEAR LAYERS WITH APPLICATION TO CARBON NANOTUBES
Recent modeling of multi-walled carbon nanotubes by a series of elastically connected Euler-Bernoulli beams has led to predictions of frequencies and mode shapes for non-coaxial modes of vibration. Whereas previous work assumes the van der Waals forces between atoms are modeled by elastic layers, this work assumes such forces are modeled by a flexible layer with quadratic nonlinearities. The nonlinear terms are derived from an expansion of the Lennard-Jones potential function for small changes from an equilibrium position. The current work assumes a model for the free vibrations of multi-walled carbon nanotubes of the free vibrations of a series of Euler-Bernoulli beams connected by flexible layers with quadratic nonlinearities. The method of multiple scales is used to derive uniformly valid asymptotic expansions for the free responses of the beams. Secular terms arising from internal resonances are identified and eliminated. The resulting equations for amplitude and phase are solved numerically. An example is presented. The results can be used to refine predictions of free responses of carbon nanotubes. The work can be extended to identify the effects of combination resonances resulting from harmonic excitation.
School:The University of Akron
School Location:USA - Ohio
Source Type:Master's Thesis
Keywords:non linear vibrations of beams with application to nanotubes
Date of Publication:01/01/2006