Wave motion in auxetic solids

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Abstract

The effect of auxeticity on the velocity of elastic wave propagation is investigated herein for isotropic solids. Three types of dimensionless wave velocities are proposed for investigating longitudinal waves in prismatic bars, plane waves of dilatation, plane waves of distortion, and surface waves. Results show that the velocity of surface waves is slightly less than that of plane waves of distortion for conventional solids, but the difference becomes large for auxetic solids. The velocity of longitudinal waves in prismatic bars is higher than that of plane waves of distortion for conventional solids but the gap narrows for solids of the low auxetic range of −0.5 < ν < 0. The velocity of longitudinal waves in prismatic bars become lower than that of plane waves of distortion for intermediate auxetic range of −0.733 < ν < −0.5, and lower than that of surface waves for high auxetic range of −1 < ν < −0.733.

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