Localized modes in a one-dimensional diatomic chain of coupled spheres

This paper presents the propagation of waves along a one-dimensional “diatomic” chain made up to welded spheres, i.e., with two steel spheres of different diameters alternating. First, a theoretical analysis is presented, which gives the vibration modes of an infinite chain, leading to two low-frequency branches, separated by a band gap. A theoretical analysis is then performed on a finite chain, containing an even or an odd number of spheres. Depending on the parity of the number of spheres in the finite chain and on the ratio between the masses of the spheres, it points out that localized modes may appear in the band gap. The theoretical results have been validated by a comparison between numerical and experimental results. Many applications of such systems can therefore be found: acoustic filters, noise and vibration isolation, acoustic wave guiding, etc.