Wave propagation in carbon nanotubes under shear deformation

This paper reports the results of an investigation on the effect of shear deformations on wave propagation in carbon nanotubes embedded in an elastic matrix. A multi-walled carbon nanotube is considered as a multiple shell coupled together through van der Waals forces between two adjacent tubes. The surrounding matrix is considered as a spring element defined by the Winkler model. Using the variational calculus of Hamilton's principle, dynamic governing equations considering the shear deformation and rotary inertia 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 frequency and the amplitude ratio of wave propagation in multi-walled carbon nanotubes embedded in an elastic matrix, respectively. The results obtained show that wave propagation in carbon nanotubes appears in a critical frequency or a cut-off frequency for different wave modes; the effect of shear deformation decreases the value of critical frequency; the critical frequency increases as the matrix stiffness increases; the inertia rotary has an obvious influence on the wave velocity for some wave modes in the higher frequency region