Free vibration analysis of curved nanotube structures

In reality, nanotubes may not be straight structures. In this work, we study free vibration analysis of curved nanotubes based on a proposed nonlocal shell model. The free vibration of curved single-walled nanotubes (SWNTs), double-walled nanotubes (DWNTs) and multi-walled nanotubes (MWNTs) is analyzed. The governing equations of a curved nanotube are developed using the proposed nonlocal shell model based on elasticity theory of Eringen. Governing differential equations of motion are simplified to the ordinary differential equations using Fourier series expansion. And solutions are obtained by applying Galerkin method. Results obtained by the present model are verified by those presented in the literature. The numerical results demonstrate the effects of the curved nanotube length, thickness, bend angle and nonlocal parameter on the natural fundamental frequency.