Band Gaps Of Two-dimensional Phononic Crystals Research Articles

Quasi-superhydrophobic microscale two-dimensional phononic crystals of stainless steel 304

Fabrication of metallic phononic and photonic crystals of characteristic size between 10 and 1000μm remains a challenge in precision using the conventional machining processes or too tedious for the cleanroom-based processes. We report the fabrication and elastodynamic bandgaps of two-dimensional phononic crystals (PhCs) machined on stainless steel 304 (SS304) substrates using the wire-electrochemical micromachining (wire-ECMM) process. Square arrays of pillars of length 400μm and cross section either 350×350μm2 or 250×250μm2 with periods 650 and 550μm, respectively, were micromachined on an SS304 homogeneous substrate. Based on these arrays, three types of PhCs were considered: air-SS304, water-SS304, and epoxy-SS304, where air, water, and epoxy are the hosts and SS304 pillars are the scatterers. We found that texturing the surface increased the contact angle of a 5-μl-water-droplet from 97.9° for an untextured SS304 substrate to a maximum of 145° for SS304 PhCs, making the latter quasi-superhydrophobic. Dispersion relations evaluated using the finite-element method revealed the presence of partial bandgaps in the 0.1–2.7 MHz for all PhCs and a complete bandgap for the epoxy-SS304 PhCs. Transmittance spectrums for incident plane waves also provided evidence for the occurrence of bandgaps. Furthermore, the buckling analysis indicated that these pillars do not undergo buckling until yield—making them mechanically robust.

Research on bandgaps in two-dimensional phononic crystal with two resonators

In this paper, the bandgap properties of a two-dimensional phononic crystal with the two resonators is studied and embedded in a homogenous matrix. The resonators are not connected with the matrix but linked with connectors directly. The dispersion relationship, transmission spectra, and displacement fields of the eigenmodes of this phononic crystal are studied with finite-element method. In contrast to the phononic crystals with one resonators and hollow structure, the proposed structures with two resonators can open bandgaps at lower frequencies. This is a very interesting and useful phenomenon. Results show that, the opening of the bandgaps is because of the local resonance and the scattering interaction between two resonators and matrix.An equivalent spring-pendulum model can be developed in order to evaluate the frequencies of the bandgap edge. The study in this paper is beneficial to the design of opening and tuning bandgaps in phononic crystals and isolators in low-frequency range.

Bandgaps of Two-Dimensional Phononic Crystals With Sliding Interface Conditions

In the present paper, the Dirichlet-to-Neumann map method is employed to compute the band structures of two-dimensional phononic crystals with smoothly sliding connection conditions between the matrix and the scatterers, which are composed of square or triangular lattices of circular solid cylinders in a solid matrix. The solid/solid systems of various material parameters with sliding interface conditions are considered. The influence of sliding interface conditions on the band structures is analyzed and discussed. The results show that the smoothly sliding interface condition has significant effect on the band structure.

Large bandgaps of two-dimensional phononic crystals with cross-like holes

In this paper we study the bandgap properties of two-dimensional phononic crystals with cross-like holes using the finite element method. The influence of the geometry parameters of the holes on the bandgaps is discussed. In contrast to a system of square holes, which does not exhibits bandgaps if the symmetry of the holes is the same as that of the lattice, systems of cross-like holes show large bandgaps at lower frequencies. The bandgaps are significantly dependent upon the geometry (including the size, shape, and rotation) of the cross-like holes. The vibration modes of the bandgap edges are computed and analyzed in order to clarify the mechanism of the generation of the lowest bandgap. It is found that the generation of the lowest bangdap is a result of the local resonance of the periodically arranged lumps connected with narrow connectors. Spring-mass models are developed in order to predict the frequencies of the lower bandgap edges. The study in this paper is relevant to the optimal design of the bandgaps in light porous materials.

Bandgap calculation of two-dimensional mixed solid–fluid phononic crystals by Dirichlet-to-Neumann maps

A numerical method based on the Dirichlet-to-Neumann (DtN) map is presented to compute the bandgaps of two-dimensional phononic crystals, which are composed of square or triangular lattices of circular solid cylinders in a fluid matrix. The DtN map is constructed using the cylindrical wave expansion in a unit cell. A linear eigenvalue problem, which depends on the Bloch wave vector and involves relatively small matrices, is formulated. Numerical calculations are performed for typical systems with various acoustic impedance ratios of the solid inclusions and the fluid matrix. The results indicate that the DtN-map based method can provide accurate results for various systems efficiently. In particular it takes into account the fluid–solid interface conditions and the transverse wave mode in the solid component, which has been proven to be significant when the acoustic impedance of the solid inclusions is close to or smaller than that of the fluid matrix. For systems with an acoustic impedance of the inclusion much less than that of the matrix, physical flat bands appear in the band structures, which will be missed if the transverse wave mode in the solid inclusions is neglected.