Binary collision approximation for multi-decorated granular chains
We study pulse propagation along decorated tapered granular chains without precompression. Our goal is to generalize the results obtained in our previous work, by analyzing a decorated chain with an arbitrary number of small grains between the large ones. Making use of an effective description, where the original decorated tapered chain is replaced by a non-decorated tapered chain with effective masses interacting via an effective potential, and applying the binary collisions approximation, we calculate the residence time of the pulse on each effective large grain. We also present the comparison between the numerical integration of the equations of motion and our analytical predictions which show the agreement to be very good for the pulse velocity, albeit only qualitatively for the velocity of the grains.