In this paper, we numerically solve the elastic multiple impact problem in a linear chain of balls using the impulse-momentum and the 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 with the aid of the Hertz method to obtain the ICRs. We use numerical analysis to demonstrate that one can significantly improve the energy absorption by placing small balls in specific locations in a linear chain of particles.

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