Longitudinal Wave Propagation in Axially Graded Raylegh–Bishop Nanorods

Longitudinal wave propagation in axially graded nanotubes was explored. The effect of shear deformation and lateral inertia on nanorods was considered using the nonlocal Raylegh–Bishop rod theory. As a novel approach, a nonlocal parameter was assumed in the graded formulation. The higher order Haar wavelet method was utilized for solving the governing equation of motion. The effects of material grading power-law index and nonlocal parameters on the longitudinal wave response of axially graded nanorods were investigated. Phase and group velocity variations of the axially graded nanorod were obtained. The present study may be useful in the modeling of advanced functional composite nanowires.