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

Abstract

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.