Demonstration of Dispersive Rarefaction Shocks in Hollow Elliptical Cylinder Chains

H. Kim, E. Kim, C. Chong, P. G. Kevrekidis, and J. Yang

Phys. Rev. Lett. 120, 194101 – Published 11 May 2018

Abstract

We report an experimental and numerical demonstration of dispersive rarefaction shocks (DRS) in a 3D-printed soft chain of hollow elliptical cylinders. We find that, in contrast to conventional nonlinear waves, these DRS have their lower amplitude components travel faster, while the higher amplitude ones propagate slower. This results in the backward-tilted shape of the front of the wave (the rarefaction segment) and the breakage of wave tails into a modulated waveform (the dispersive shock segment). Examining the DRS under various impact conditions, we find the counterintuitive feature that the higher striker velocity causes the slower propagation of the DRS. These unique features can be useful for mitigating impact controllably and efficiently without relying on material damping or plasticity effects.

Received 23 October 2017

DOI:https://doi.org/10.1103/PhysRevLett.120.194101

Physics Subject Headings (PhySH)

Classical mechanics

Nonlinear waves

Nonlinear Dynamics

Authors & Affiliations

H. Kim¹, E. Kim^1,2, C. Chong³, P. G. Kevrekidis⁴, and J. Yang^1,*

¹Aeronautics and Astronautics, University of Washington, Seattle, Washington, 98195-2400, USA
²Division of Mechanical System Engineering & Automotive Hi-Technology Research Center, Chonbuk National University, 567 Baekje-daero, Deokjin-gu, Jeonju, Jeonbuk 54896, Republic of Korea
³Department of Mathematics, Bowdoin College, Brunswick, Maine 04011, USA
⁴Department of Mathematics and Statistics, University of Massachusetts, Amherst, Massachusetts 01003, USA