Longitudinal wave motion in width-constrained auxetic plates

Abstract

This paper investigates the longitudinal wave velocity in auxetic plates in comparison to conventional ones, in which the plate is constrained from motion in the width direction. By taking into account the thickness change of the plate and its corresponding change in density, the developed wave velocity is casted not only as a function of Young’s modulus and density, but also in terms of Poisson’s ratio and longitudinal strain. Results show that density and thickness variations compensate for one another when the Poisson’s ratio is positive, but add up when the Poisson’s ratio is negative. Results also reveal that the classical model of longitudinal wave velocity for the plate is accurate when the Poisson’s ratio is about 1/3; at this Poisson’s ratio the influence from density and thickness variations cancel each other. Comparison between the current corrected model and the density-corrected Rayleigh–Lamb model reveals a number of consistent trends, while the discrepancies are elucidated. If the plate material possesses a negative Poisson’s ratio, the deviation of the actual wave velocity from the classical model becomes significant; auxeticity suppresses and enhances the wave velocity in compressive and tensile impacts, respectively. Hence the use of the corrected model is proposed when predicting longitudinal waves in width-constrained auxetic plates, and auxetic materials can be harnessed for effectively controlling wave velocities in thin-walled structures.