Band structure of elastic bodies with periodic nonlocalities

Investigating the status of travelling waves in systems integrated with periodic means of distant communication, and the possibility of obstructing the energy flow carried via coupled modes, are of interest. The governing system of linear differential equations with periodic coefficients gives the possibility to adopt Floquet theorem, as a powerful framework, to identify the location of stop band frequencies. The generation of gaps in the band structure of the system owing to the newly launched periodic long-range channels is shown. The likelihood of pulling the first stopband to lower frequency bands as a major demand, is examined by raising some assumptions.