We study momentum and energy propagation in 1D tapered chains of spherical granules which interact according to a Hertz potential. In this work we apply the binary collision approximation, which is based on the assumption that transfer of energy along the chain occurs via a succession of twoparticle collisions. Although the binary theory correctly captures the trends of increase or decrease of kinetic energy and momentum, the actual values of these quantities are not in good quantitative agreement with those obtained by numerically integrating the full equations of motion. To address this difficulty we have developed a mixed numerical/analytical correction algorithm to provide an improved estimate of the velocity of the particles during pulse propagation. With this corrected velocity we are in turn able to correctly predict the momentum and kinetic energy along the chain for several tapering configurations, specifically for forward linear, forward exponential, backward linear and backward exponential tapering.

We study via numerical simulations a granular chain not only with decreasing radii (forward tapering) in geometric progression, but also decorated with grains positioned on the top and bottom of the chain, without altering its original length. The decorating grains act as an auxiliary chain which traps part of the energy and linear momentum, both propagating as a pulse due to disturbances produced at the end of the chain. Thus, this configuration optimizes the impact attenuation and aligns the chain naturally (by symmetry) which facilitates the construction of the experimental setup. Furtheremore, since the decorating grain radii increase along the chain, this new type of chain is necessarily short in order to avoid precompression. Nevertheless, even with short chains, it is possible to mitigate impacts almost completely.

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