Band structure analysis of a thin plate with periodic arrangements of slender beams

On the Mechanism of Bandgap Formation in Beams With Periodic Arrangement of Beam-Like Resonators

“…The authors suggest that the resonant frequency of the resonators does not necessarily lie in a band gap. Serrano et al [2] also showed this behavior for a system composed by a plate as substrate and different arrangements of beam-resonators joined to it. In the cited work, the band gaps do not appear at the natural frequencies of the beams working under bending vibration.…”

“…In the cited work, the band gaps do not appear at the natural frequencies of the beams working under bending vibration. A brief remark of this singularity on the band gap formation is made on [2,13]. Thus, in the current work, we give a extended analysis focusing on the role of resonator natural frequencies on the band structure of the whole system.…”

“…Among the great variety of metastructures, systems composed by a substrate (plate or beam) and an array 25 of spring-mass resonators periodically joined to it have 26 been commonly investigated [3][4][5]. Moreover, studies 27 related to systems with beams working as resonators 28 instead of the spring-mass ones have been developed by 29 several authors [2,[6][7][8][9].…”

“…We are going to apply Bloch's theorem [1,2] to the 132 representative unit cell (Fig. 1b) which defines the lat-133 tice structure.…”