Wave propagation in carbon nanotubes under shear deformation

Abstract

This paper reports the results of an investigation on the effect of shear deformations onwave propagation in carbon nanotubes embedded in an elastic matrix. A multi-walledcarbon nanotube is considered as a multiple shell coupled together through van der Waalsforces between two adjacent tubes. The surrounding matrix is considered as a springelement defined by the Winkler model. Using the variational calculus of Hamilton’sprinciple, dynamic governing equations considering the shear deformation and rotaryinertia terms are derived. Numerical examples describe the effects of shear deformation,rotary inertia and elastic matrix on the velocity, the critical frequency, the cut-off frequencyand the amplitude ratio of wave propagation in multi-walled carbon nanotubes embeddedin an elastic matrix, respectively. The results obtained show that wave propagation incarbon nanotubes appears in a critical frequency or a cut-off frequency for different wavemodes; the effect of shear deformation decreases the value of critical frequency; the criticalfrequency increases as the matrix stiffness increases; the inertia rotary has an obviousinfluence on the wave velocity for some wave modes in the higher frequency region.