LAUSR

Dynamic behavior of single walled carbon nanotubes (CNTs) delivering a nanoparticle with constant velocity is investigated subject to various boundary conditions. The governing equation is derived based on nonlocal Euler–Bernoulli beam theory. The Vander Waals force is taken into account using a confined spring connecting the nanoparticle to the CNT. Furthermore, the effect of surrounding are modeled as elastic foundation. Besides, a mixed Galerkin-differential quadrature (DQ) method is introduced to solve the problem. First, the partial differential equation is converted to a set of ordinary differential equations by applying Galerkin method and then a step-by-step differential quadrature method utilized to solve the set. The solution is verified by comparing the results with the exact solution for double simply-supported CNT and a great agreement is achieved. Furthermore, the convergence of the method is studied. Then, the time history of the CNT’s vibration is provided via 3-D figures for a case study. Moreover, the effects of particle’s velocity on maximum deformation of the CNT for several boundary conditions are investigated and the critical speeds are estimated.