Platonic crystal with low-frequency locally resonant snail structures. Wave trapping, transmission amplification and shielding
arXiv:1802.08316 · doi:10.1016/j.jmps.2018.08.017
Abstract
We propose a new type of platonic crystal. The proposed microstructured plate includes snail resonators with low-frequency resonant vibrations. The particular dynamic effect of the resonators are highlighted by a comparative analysis of dispersion properties of homo- geneous and perforated plates. Analytical and numerical estimates of classes of standing waves are given and the analysis on a macrocell shows the possibility to obtain localization, wave trapping and edge waves. Applications include transmission amplification within two plates separated by a small ligament. Finally we proposed a design procedure to suppress low frequency flexural vibration in an elongated plate implementing a by-pass system re- routing waves within the mechanical system.
11 figures (20 files)
References in corpus (7)
- Inertial amplification of continuous structures: Large band gaps from small masses
- Transformation elastodynamics and cloaking for flexural waves
- Cymatics for the cloaking of flexural vibrations in a structured plate
- Transformation cloaking and radial approximations for flexural waves in elastic plates
- Trapped Modes and Steered Dirac Cones in Platonic Crystals
- Dynamic interfacial trapping of flexural waves in structured plates
- Moulding flexural waves in elastic plates lying atop a Faqir's bed of nails