  A systematic method for optimal design of layered periodic composites for
mitigation of impact-induced shock waves is presented. Frequency spectrum of a
pulse with a sharp rise-time is analyzed and the frequency range that carries
most of the pulse energy is identified. A genetic algorithm is used to maximize
the stop bands of a layered periodic composite over the target frequency range.
Due to reflection of the pulse over the stop bands, the maximum stress and the
energy of transmitted pulse become minimal. To verify the theoretical
calculation a sample is fabricated and Hopkinson bar experiments are performed.
It is observed that only 9.7% of energy of the incident pulse gets transmitted
through the sample. In addition, the wave speed in the composite is measured to
be 45.4% less than the wave speed in its constituent material with the lowest
wave speed.
