14. Longitudinal Waves in Auxetic Solids

This chapter considers the effect of Poisson’s ratio on lateral deformation in longitudinal waves in prismatic bars, and the consequent density change. A non-dimensionalization is adopted herein such that the dimensionless velocity of longitudinal wave is constant with Poisson’s ratio. Based on this non-dimensionalization, incorporation of density correction and/or lateral inertia using the strength of materials approach gives a dimensionless velocity that decreases and increases with Poisson’s ratio for tensile and compressive loads, respectively, such that the pivot conditions take place at v = 0.5 considering density correction only, at v = 0 considering lateral inertia only, and at v = 0.25 considering both corrections. An analogy is then extended to the case of plane waves of dilatation, in which only density correction is required. Thereafter, a revisit to the lateral inertia of Love rods provides the combined effect of density, Young’s modulus, Poisson’s ratio, polar radius of gyration and wave number on the velocity of longitudinal waves in Love rods.