Structural instability of carbon nanotubes embedded in viscoelastic medium and subjected to distributed tangential load

In this paper, the nonlocal Euler-Bernoulli beam model is used to predict the static and dynamic structural instability of carbon nanotubes (CNTs) subjected to a distributed tangential compressive load. The CNT is considered to be embedded in a Kelvin-Voigt viscoelastic medium. Equation of motion and boundary conditions are obtained using the extended Hamilton's principle and the extended Galerkin's method is applied in order to transform the resulting equations into a general eigenvalue problem. The derived equations are validated by comparing the results achieved from the new derivations with existing solutions in literature. Effects of several experimentally interesting boundary conditions are considered on the stability characteristics of the CNT. Moreover, the influences of small scale parameter and material properties of the surrounding viscoelastic medium on the stability boundaries are examined.