Modal analysis of double-walled carbon nanocones using the finite element method

The vibrational properties of double-walled carbon nanocones are investigated herein. The double-walled carbon nanocones with different geometries including apex angles and lengths are considered. The simply supported-simply supported, clamped-free and clampedclamped boundary conditions are applied on the nanocones. A linear elastic beam-based finite element method is employed to obtain the frequencies of the double-walled carbon nanocones. Elastic beam elements are used to model the carbon-carbon bond in the structure of the nanocones. Besides, the spring elements are employed to describe the nonbonding van der Waals interactions between different layers. Natural frequencies and mode shapes of the double-walled carbon nanocones are extracted by solving the eigenvalue problem. It is observed that increasing the disclination angle of nanocones increases their natural frequency. However, increasing the nanocones height leads to decreasing the frequency.