On the existence of subresonance generated in a one-dimensional chain of identical spheres

In this paper, the propagation of short compressional pulses through a one-dimensional chain of identical spherical beads is analyzed. First, a single sphere is studied. Then, an infinite chain of identical spheres is considered. Finally, a finite linear chain can be seen as a particular case of an infinite chain. It shows the existence of allowed and forbidden frequency bands. In the case of a finite chain of spheres, discrete resonance frequencies are excited and may be identified as "subresonance" of modes observed with a single sphere. We also analyze how the coupling between two adjacent spheres and the number of beads in the chain, modify the degeneracy of the stationary states. Finally, the theoretical results are qualitatively verified with experimental data obtained with the "resonant sphere technique."