| Using eigenvalue analysis of the mass and stiffness matrices, directly computed from atomistic simulations, natural frequencies and mode shapes of various carbon nanotubes (CNTs) are studied. The stiffness matrix is developed from the Tersoff-Brenner potential for carbon-carbon interactions. The computed frequencies of the radial breathing modes of a variety of armchair (n, n) nanotubes agree well with results obtained by others using different techniques. In addition, the present work discusses diverse mode shapes such as: accordion-like axial modes, lateral bending modes, torsional modes, axial shear modes, and radial breathing modes for a variety of single-wall, multi-wall, and bamboo type CNTs. The effects of different boundary conditions of the CNT on the computed frequencies and mode shapes have been investigated for possible applications in vibration sensors or electromechanical resonators. |
