On wave propagation of porous nanotubes

An analytic model of porous nanotubes for the wave propagation analysis is formulated with the help of the nonlocal strain gradient theory. The dispersion relations between phase velocity and wave number is determined by solving an eigenvalue problem. It is found that the asymptotic phase velocity can be increased by increasing the strain gradient parameter or decreasing the nonlocal parameter. In addition, the heterogeneity of functionally graded materials and temperature variation have a substantial influence on the dispersion relations of nanotubes. The nonlocal parameter and strain gradient parameter have significant effects on the dispersion relation at high wave numbers, in contrast, this effects can be negligible at low wave numbers. Meanwhile, it can be inferred that the phase velocity can decrease or increase as the porosity volume fraction rises, which depends on the power law index.