Noncoaxial vibration and buckling analysis of embedded double-walled carbon nanotubes by using doublet mechanics

Free vibration and buckling of double-walled carbon nanotubes embedded in an elastic medium with simply supported boundary conditions are studied. Doublet Mechanics (DM) is used in the analysis. Macro level strains and stresses are defined in terms of micro level strains and stresses in the DM theory. These micro deformations and micro stresses are expanded in Taylor series and the number of terms in the Taylor series defines degree of the approach. Double-walled carbon nanotubes are modelled as Euler-Bernoulli beams embedded in an elastic medium. Critical buckling loads and free vibration frequencies are obtained by using DM and compared with the classical elasticity solutions. It is obtained that for some frequencies carbon nanotubes move noncoaxially. Noncoaxial vibration and buckling affect the physical properties of carbon nanotubes. The present results show that a length scale dependent DM can be used in the design of nano electro-mechanical systems.