Wave propagation in multiwall carbon nanotubes embedded in a matrix material

This paper presents an analytical method to investigate wave propagation in individual multiwall carbon nanotubes (MWNTs) or MWNTs embedded in an elastic matrix, by using a laminated cylindrical shell mode. Each of the concentric tubes of the MWNTs is an individual elastic shell and coupled with adjacent tubes through van der Waals interaction. The effect of matrix surrounding MWNTs is considered as a spring defined by the Winkler model. The disperse curves are obtained by solving an eigenvalue problem. The wave propagation characteristics and the amplitude radio between two walls of MWNTs are described by using the dispersive curves. Results show that the matrix surrounding MWNTs takes an increase in the threshold frequency of wave propagation in the MWNTs, and the effect of matrix stiffness on the velocity and the amplitude ratio between two walls of wave propagation in MWNTs embedded in an elastic matrix is dependent on wave modes.