Longitudinal Wave Velocity in Auxetic Rods

This short brief develops a model for the velocity of longitudinal wave propagation in auxetic rods. Due to the large density change in auxetic solids and significant lateral deformation for Poisson's ratio between −1 and −0.5, this note takes into consideration density correction and lateral inertia. Results show that deviation from the elementary wave propagation model becomes more significant the more the Poisson's ratio of the rod material deviates from 1/4, in which the deviation of wave velocity is insignificant for Poisson's ratio in the positive range, but significant in the negative range. Specifically, the tensile and compressive wave velocity increases and decreases, respectively, for Poisson's ratio less than 1/4, but this trend reverses for Poisson's ratio greater than 1/4. In addition to showing that the elementary wave propagation model is invalid for describing the longitudinal wave velocity in auxetic rods, the results also suggest that auxetic materials are useful for applications that require slowing down and speeding up of compressive and tensile wave propagations, respectively.