Technical Brief

Longitudinal Wave Velocity in Auxetic Rods

[+] Author and Article Information
Teik-Cheng Lim

School of Science and Technology,
SIM University,
461 Clementi Road,
Singapore S599491
e-mail: alan_tc_lim@yahoo.com

Contributed by the Materials Division of ASME for publication in the JOURNAL OF ENGINEERING MATERIALS AND TECHNOLOGY. Manuscript received May 23, 2014; final manuscript received December 15, 2014; published online January 30, 2015. Assoc. Editor: Vadim V. Silberschmidt.

J. Eng. Mater. Technol 137(2), 024502 (Apr 01, 2015) (3 pages) Paper No: MATS-14-1113; doi: 10.1115/1.4029531 History: Received May 23, 2014; Revised December 15, 2014; Online January 30, 2015

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.

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Grahic Jump Location
Fig. 1

Schematic adopted for analysis of longitudinal wave motion with lateral inertia (without lateral inertia, the cross-sectional area is assumed A0 throughout the entire rod)

Grahic Jump Location
Fig. 2

Effect of auxeticity and longitudinal strain on dimensionless wave velocity considering lateral inertia and density correction

Grahic Jump Location
Fig. 3

Auxetic and conventional regions for the dimensionless velocity of a longitudinal wave in a prismatic bar



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