Quantitative analysis of the vibration modes in a finite set of coupled spheres

This paper deals with the propagation of waves along a one-dimensional chain made up of welded spheres. First, a theoretical analysis allows the vibration modes of the chain to be quantitatively described. It has been validated by a comparison between numerical results, using the finite element method and experimental results, restricted to sets of two or three coupled spheres. It is numerically and experimentally verified that the peaks associated with the Rayleigh modes broaden out as the mode number increases and that the passband structure is strongly influenced by the characteristics of the welding between the cells of the periodic structure. The interest of such an approach is then illustrated by the examination of an inverse problem, in which the analytical model is used to deduce the characteristics of the welding.