Nonlocal frequency analysis of embedded single-walled carbon nanotube using the Differential Quadrature Method

In the present paper free vibrations of embedded single-walled carbon nanotubes based on local Euler-Bernoulli beam theory are investigated. The surrounding elastic medium is described as the Winkler and Pasternak models, defined by the kw and kp coefficients. The Hamilton principle is applied to derive the governing equations and boundary conditions, which are solved by using the well-known Differential Quadrature Method (DQM). The influence of the elastic medium coefficients, nonlocal parameter and end supports on the free vibrations characteristics of the single-walled carbon nanotube (SWCNT) is described. Numerical examples are performed to show the accuracy of the proposed method.