Nonlocal effects in the forced vibration of an elastically connected double-carbon nanotube system under a moving nanoparticle

This study presents an analytical method for the forced vibration of an elastically connected double-carbon nanotube system (DCNTS) carrying a moving nanoparticle based on the nonlocal elasticity theory. The two nanotubes are identical and are connected with each other continuously by elastic springs. The problem is also solved numerically by using the Galerkin method and the time integration method of Newmark to establish the reliability of the analytical method. Two sets of critical velocity exist for DCNTS. The closed-form solutions for the dynamic deflections of the two nanotubes are derived for these two sets of critical velocity for the first time in this study. The influences of the nonlocal parameter, aspect ratio, velocity of the moving nanoparticle and the elastic layer between the nanotubes on the dynamic responses are discussed. The study shows that the dynamic behavior of the double-carbon nanotube system is greatly influenced by the nonlocal effects. The dynamic deflections predicted by the classical theory are always smaller than those predicted by the nonlocal theory due to the nonlocal effects. Thus, the classical beam models are not suitable in modeling carbon nanotubes with small aspect ratio, and nonlocal effects should be taken into account. Furthermore, the velocity of the nanoparticle and the stiffness of the elastic layer have significant effects on the dynamic behavior of DCNTS.

► An analytical method is proposed for the vibration of an elastically connected double-carbon nanotube system under a moving nanoparticle. ► Two sets of critical velocity are found for the double-carbon nanotube system. ► Dynamic deflections predicted by the classical theory are always smaller than those obtained by the nonlocal theory. ► The deflections of the primary and the secondary nanotube become to equal to each other in the case of rigid coupling. ► In the case of the weak elastic coupling, the secondary nanotube has the positive and the negative deflections as if it vibrates under a moving harmonic load.