In this paper, axisymmetric vibrational characteristics of multiwalled carbon nanotubes (MWCNTs) with finite length are examined by continuum mechanics elastic shell model. Linearized analysis is used to model the van der Waals interaction between adjacent tubes. By applying the Rayleigh-Ritz technique to the system of the Navier equations, weak formulations are derived and two-dimensional finite element model is developed. By calculating the eigenvalues and eigenvectors, the axisymmetric natural frequencies and mode shapes of the MWCNTs are obtained. In order to verify the correctness of the results in this paper, radial breathing mode (RBM) frequencies of carbon nanotubes (CNTs) given by the present method compared with those obtained by other investigators. One of the focuses of this work is investigation of effects of dimensional parameters (such as length, diameter, as well as number of layers of MWCNTs) and end conditions (such as free-free and clamped supports) on axisymmetric vibrations of MWCNTs. In this analysis, a proportion factor between longitudinal frequencies and the length of CNT is found. By comparing this factor with those obtained from the classic equation, an updated value for effective Young’s modulus of CNTs is suggested. The effects of van der Waals forces on radial vibration of MWCNTs are also explained and found that the van der Waals forces moderately increase radial frequencies of one layer of MWCNTs comparing with considering that layer as an individual tube.

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