Low frequency vibration of multiwall carbon nanotubes with heterogeneous boundaries

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Abstract
Heterogeneous end constraints are imposed on multiwall carbon nanotubes (MWCNTs) by sequentially clamping one end of their originally simply supported constituent tubes. The finite element method is employed to study the vibration of such MWCNTs with an emphasis on the effect of the mixed boundary conditions. The results show that the clamping process constantly enhances the dynamic stiffness of MWCNTs, which leads to substantial frequency increase up to 50% and, in some cases, the transformation of the fundamental vibration mode. In particular, the vibration frequency is always found to be most sensitive to fixing the outermost tubes, showing the critical role of this individual tube in determining the structural stiffness of the whole MWCNTs as a coupled system.

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