Axial dynamics of a nanorod embedded in an elastic medium using doublet mechanics

Abstract

This study investigates the axial vibration of carbon nanotubes (CNTs) embedded in an elastic medium using scale dependent doublet mechanics (DM) theory. Governing equations and all boundary conditions of CNTs are derived based on the variational principle. Free vibration frequencies are obtained and compared with the classical elasticity results for clamped-clamped (C-C) and clamped-free (C-F) boundary conditions. The effect of elastic medium stiffness, nanorod length and doublet separation distance on the axial vibration is examined. It is obtained that important differences exist between vibration frequencies predicted by classical elasticity theory and DM. DM theory can be used in the nano length scale design of structures. (C) 2016 Elsevier Ltd. All rights reserved.