Abstract
A nonlocal theory of elasticity is developed to study free vibration of rotating single walled carbon nanotubes (SWCNTs) with different boundary conditions. The equations of motion are obtained applying Hamilton’s concept, which contain the nonlocal Eringen’s theory of elasticity, Love’s shell assumptions, the influence of the centrifugal and the Coriolis accelerations, and the preliminary hoop stress. The equations of motion as well as the boundary condition equations are transformed into a set of algebraic equation applying Fourier decomposition and the DQ method in the longitudinal direction. Numerical results, presented for the frequency parameters and the associated vibration wavenumbers of a series of SWCNT and with different nonlocal parameters, confirm the validity of the solution presented. Furthermore, the model is used to clarify the effects of rotating speed, boundary conditions, length-to-radius ratio and nonlocal parameter on the natural frequency.
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