Analytical analysis for the forced vibration of CNT surrounding elastic medium including thermal effect using nonlocal Euler-Bernoulli theory

This article studies the free and forced vibrations of the carbon nanotubes CNTs embedded in an elastic medium including thermal and dynamic load effects based on nonlocal Euler- Bernoulli beam. A Winkler type elastic foundation is employed to model the interaction of carbon nanotube and the surrounding elastic medium. Influence of all parameters such as nonlocal small-scale effects, high temperature change, Winkler modulus parameter, vibration mode and aspect ratio of short carbon nanotubes on the vibration frequency are analyzed and discussed. The non-local Euler-Bernoulli beam model predicts lower resonance frequencies. The research work reveals the significance of the small-scale coefficient, the vibrational mode number, the elastic medium and the temperature change on the non-dimensional natural frequency.