Free vibrations of single walled carbon peapods

• A nonlocal continuum model is developed for the lateral vibrations of nano-peapods resting on Winkler foundations.
• The small scale effects on the fundamental frequency is investigated and it is found that it may increase or decrease the fundamental frequency depending upon the foundation stiffness value.
• For any mass ratio there exist a certain foundation stiffness for which the fundamental frequency is independent of the small scale effect.

In this paper the free vibration of single walled carbon nanopeapods encapsulating C60C60 molecules is considered. The nanopeapod is embedded in an elastic medium and clamped at both ends. The Euler–Bernoulli beam model is used for the carbon nanotube and the C60C60 molecules are considered as lumped masses attached to the beam. Based on the nonlocal elasticity theory the governing equation of motion is derived and the resonance frequencies of the nanopeapod are obtained. The effects of small scale, foundation stiffness and ratio of the fullerenes' mass to the nanotube's mass on the frequencies are studied and some conclusions are drawn.

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