On the gradually vanishing bandgaps of periodic locally resonant metamaterial Timoshenko beams in the high frequency limit
Journal
Physics Letters, Section A: General, Atomic and Solid State Physics
Journal Volume
420
Start Page
127757
ISSN
03759601
Date Issued
2021
Author(s)
Xu, Shaofeng
Abstract
Contrary to the perpetual-existed Bragg bandgaps in phononic crystals, the Bragg (BG) bandgaps in a periodic locally resonant (LR) metamaterial will gradually vanish in the high frequency limit. In this short discussion, from a mathematical perspective, we explain the physical phenomenon of the vanishing high-frequency bandgaps. To allow the model to be more practical while being general, a beam with periodic local resonators (i.e., LR+BG bandgaps) and a beam with concentrated masses (i.e., BG bandgaps only) are considered. In addition, to avoid high-frequency discrepancies caused by the unreasonably rapid increasing wave velocity in a Euler beam, a Timoshenko beam model considering shear deformation and rotary inertia is considered. Based on our analytical derivations, the transition behavior between the LR and Bragg bandgaps is also explored.
Subjects
Bandgap Transition
Bragg Bandgaps
Local Resonance Bandgaps
Metamaterials
Phononic Crystals
Publisher
Elsevier B.V.
Type
note