This work describes a novel modelling scheme to elucidate the frequencies of carbon nanotubes via continuum mechanics by considering the van der Waals force interaction based on differential quadrature simulations, in which nanobeam-bending paradigms are utilized. Exactly how the surrounding elastic medium, length-to-radius ratio, and van der Waals forces of the carbon nanotubes affect the frequencies is also investigated. The proposed modelling scheme is highly promising for advanced carbon nanotube applications. Further elucidation of the vibration mechanism of carbon nanotubes embedded in an elastic medium in this work significantly contributes to efforts to design nano oscillators.
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