Non-conservative instability of cantilever carbon nanotubes resting on viscoelastic foundation

In this study, the influence of viscoelastic foundation on the non-conservative instability of cantilever Carbon nanotubes (CNTs) under the action of concentrated follower force is investigated. The Kelvin–Voigt, Maxwell and Standard linear solid types of viscoelastic foundations are utilized to model the interaction between CNT and surrounding viscoelastic medium. The governing equations of motion and boundary conditions are obtained based on the nonlocal Euler–Bernoulli theory using Hamiltonʹs principle. Applying the Galerkin approach, the resulting equations are transformed into a set of eigenvalue equations. The validity of the present analysis is confirmed by comparing the results with those obtained in literature. The effects of the main parameters on the stability characteristics of the CNT are also elucidated. Most results presented in this paper have been absent from the literature for the instability of the CNT subjected to follower force.