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Research Papers

# Shock Absorption Using Linear Particle Chains With Multiple Impacts

[+] Author and Article Information
Mohamed Gharib

Department of Mechanical Engineering, Southern Methodist University, Dallas, TX 75275mgharib@smu.edu

Ahmet Celik

Department of Mechanical Engineering, Yildiz Technical University, Besiktas, Istanbul 80750, Turkeyacelik@yildiz.edu.tr

Yildirim Hurmuzlu1

Department of Mechanical Engineering, Southern Methodist University, Dallas, TX 75275hurmuzlu@lyle.smu.edu

1

Corresponding author.

J. Appl. Mech 78(3), 031005 (Feb 07, 2011) (9 pages) doi:10.1115/1.4003349 History: Received September 29, 2009; Revised September 27, 2010; Posted January 04, 2011; Published February 07, 2011; Online February 07, 2011

## Abstract

In this paper, we numerically solved the elastic multiple impact problem in a linear chain of balls using the impulse momentum and Hertz contact theory based methods. The first method depends on a parameter called the impulse correlation ratio (ICR) while the latter one depends on the material properties and geometries of the colliding bodies. We compared the post impact velocities from the two methods and we found that the two methods yield similar solutions for elastic collisions. Then, we develop an energy absorption scheme using an arrangement of balls with different sizes. The impulse momentum method is used and the ICRs are experimentally estimated. We use numerical and experimental analyses to demonstrate that one can significantly improve the energy absorption by placing small balls in specific locations in a linear chain of large balls.

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## Figures

Figure 2

Contact between three spherical balls

Figure 3

Velocity-impulse diagrams for three steel ball chains: m1=m2=m3=1 kg, v1−=1 m/s, v2−=v3−=0, e1,2=e2,3=1, and α2=0.1325

Figure 4

Bouncing pattern regions (4): v1−=1 m/s, v2−=v3−=0, e1,2=e2,3=0.5, and α2=0.15

Figure 5

Velocity-impulse diagrams (4): r1=r2=0.01, v1−=1 m/s, v2−=v3−=0, e1,2=e2,3=1, and α2=0.15

Figure 6

Velocity-impulse diagrams for three steel ball chains: r1=0.1, r2=0.001, v1−=1 m/s, v2−=v3−=0, e1,2=e2,3=1, and α2=0.0656

Figure 7

Two balls with signal connectors: (a) the experiment setup and (b) the electric circuit diagram

Figure 8

Signals corresponding to single and multiple impacts: (a) two ball impacts and (b) three ball impacts. Each two balls are in contact at zero voltage.

Figure 9

Arrangement of the absorption balls

Figure 10

KER for five large balls arrangement at e=0.95

Figure 11

KER for five large balls arrangement at e=0.9

Figure 12

KER for five large balls arrangement at e=0.8

Figure 13

The minimum KER for five large balls arrangement

Figure 14

The effect of the number of large balls on KER

Figure 15

The experiment setup: (a) 7L−6S arrangement and (b) details of L−S−L

Figure 16

Experimental and theoretical KER for three, four, and five large balls arrangement

Figure 1

Three ball impact

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