Abstract
Recently, the authors developed analytical expressions for the dispersions of Floquet waves that propagate in a structure consisting of a plate with multiple arrays of line attachments. The dispersions of these Floquet waves, and in particular the imaginary parts of their wavenumbers, quantify the attenuation of vibrational energy in space as the frequency of a local excitation is varied. Understanding how the parameters of the attached structures, such as their spacings and impedances, affect the Floquet wave dispersions could provide further means to include consideration of energy localization or distribution in the structural design process. Such an understanding is developed in the present work by identifying those cases in which the treatment of certain arrays can be greatly simplified. In particular, limiting cases of small and large array spacings are investigated for which the treatment of particular arrays can be greatly simplified. Such simplifications are not immediately obvious without access to analytical expressions for the Floquet wavenumbers, as the dynamics of all arrays are coupled through the plate. Results presented here will aid the structural design community by indicating which design changes most effectively control energy distribution and by indicating when simplified finite element models of multiple-array structures are possible.
