alireza fatahi-vajari - Department of Mechanical Engineering, Shah)-yar Branch, Islamic Azml University, Shahrjyar, Iran

This paper investigates the nonlinear coupled radial-axial vibration of single-walled carbon nanotubes (SWCNTS) based on Homotopy perturbation method (I-IPM). Twocoupled forth order partial differential equations that govern t.he nonlinear coupled radial-axial vibration for such nanotube is derived using nonlocal theory. The nonlinearities originated from the large deformations of tlie beam which leads to the interaction of radial-axial deformations. It is the first time that the nonlocal theory isused to analyze the nonlinear coupled radial—axial vibration of SWCNTs. To obtain the nonlinear natural frequencies in coupled radial-axial vibration mode, these couplednonlinear equations are solved using HPM. It is found that the coupled radial-axial vibrational frequencies are complicated due to coupling between two vibration modes.The influences of some commonly used botuidary conditions, changes in vibration modes and variations of the nanotubes geometrical parameters on the nonlinear coupled radial-axial vibration characteristics of SWCNTs are discussed. It is shown that boundary conditions and maximum vibration velocity play significant role in the nonlinear coupled radial-axial vibration response of SWCNTS. It was also shown that unlike the linear one, the nonlinear natural frequencies are dependent to maximum vibration velocity. Increasing the maximum vibration velocity increases the natural frequency of vibration compared to the predictions of the linear models. However,with increase in tube length, the effect of the maximum vibration velocity on the natural frequencies decreases. To show the accuracy and capability of this method, the resultsobtained herein are compared with the fourth order Runge- Kuta nttmcrical results and good agreement is observed.

nonlinear coupled axial-radial vibration,homotopy perturbation method, natural frequency, single-walled carbon nanotubes, nonlocal theory