In this paper, the flexural vibration of the curved single-walled carbon nanotube (SWCNT) is investigated, based on the nonlocal Euler-Bernoulli beam model. The SWCNT is assumed to be embedded in an elastic medium. Both Winkler-type and Pasternak-type foundation models are utilized to simulate the interaction of the SWCNT with the surrounding elastic medium. Three typical boundary conditions, namely clamped-clamped, clamped-pinned and pinned-pinned, are used to investigate the effect of the supported end conditions. Based on the Ga-lerkin method, a solution for natural frequency is obtained. According to this study, the influ-ences of the amplitude of waviness, the nonlocal effects, the Winkler modulus parameter, the Pasternak shear modulus parameter, the boundary condition and the aspect ratio are analyzed and discussed. It is shown that waviness in the curved SWCNT causes an obvious increase in the natural frequency in comparison with the straight SWCNT, especially for a compliant medium, pinned-pinned boundary condition and short SWCNT.

Keywords