This paper presents the study of propagation of elastic waves in nanostructures using continuum approximation. The
wave propagation characteristics in both 1-D and 2-D nanostructures, namely the carbon nanotubes and Graphene are
studied in this paper. In particular, the use of various gradient elasticity theories, namely the Eringen’s Stress gradient
theory, the second and fourth order strain gradient theories, that brings in atomistic length scale parameters into the
continuum governing equations, is used in this paper to study the wave propagation characteristics in the nanostructures.
Using these non-local theories, wave propagation in Single and Multi-wall carbon tubes and monolayer Graphene
structures are studied. A number of examples are presented that brings out the essential wave propagation features such
as escape frequency, cut-off frequencies, phase speeds and group speeds in these structures.