Study On Two-Dimensional Phononic Crystals Band Gap Property Based On Symmetry

Phononic crystal (PC) is a kind of artificial acoustic functional materials with periodic structures which exhibit acoustic or elastic wave band gaps (BGs). For near two decades, the study on PCs has proved to be of great interest due to their novel and unique BGs, localization and negative refraction characteristics, and their potential applications in the vibration isolation, noise control, acoustic filter, waveguide devices acoustic lens, and so on.In order to obtain low-frequency BG, two kinds of new lattices are designed based on symmetry reduction. Band structure, transmission spectra and pressure field of two-dimensional solid/fluid (air) PCs are investigated with the plane wave expansion (PWE) method and finite element method (FEM), respectively. BG and localization characteristics are measured based on ultrasonic immersion transmission technology. Main results are as follows:(1) Deaf band for square lattice steel/water PCsFor two-dimensional square lattice steel/water PCs, the measured transmission spectra are in agreement with the numerical results at low-frequency region along the two high symmetry directions in the first Brillouin zone (BZ). While along theгMdirection, the measured transmission spectra are not in accordance with the band structure calculated with the PWE at high-frequency region. The related bands are proved to be anti-symmetry mode, i.e. deaf band through calculating pressure field. Results show that there exists deaf band in square lattice steel/water PCs, and explain the mentioned disagreement.(2) As well known, bands degeneracy at high symmetry points in the first BZ plays an important role in limiting band gap open. By reducing the symmetry of lattice through introducing an additional"atom(s)"in a unit cell, bands degeneracy is lifted, and an absolute BG is obtained at low-frequency region.①BG characteristic for hybrid triangular-graphite lattice PCs. By reducing symmetry of structure, hybrid triangular-graphite lattice is considered by placing two additional"atom(s)"averagely at the diagonal of a unit cell of triangular lattice. Band structures for steel/air PCs are computed with the PWE method. Numerical results show that the location and width of stop band can be tuned by varying radii of rods at different positions. Complete BG between high-frequency bands opens easily for large radius of triangular lattice positions. In contrast, there appears wide BG between low-frequency bands easily for large radius of graphite lattice positions.②BG characteristic for hybrid triangular lattice PCs. For hybrid triangular lattice PCs, due to symmetry reduction breaking bands degeneracy at high symmetry point in the first BZ, a novel low-frequency complete BG occurs between the first and the second bands. The location and width of the BG can be tuned by altering the position of additional"atom". Measured results show that reducing symmetry is a valid method to lift bands degeneracy and open low-frequency band gap. Experimental results are basically in agreement with numerical results.(3) BG characteristic for PCs with elliptical scattersTriangular lattice steel/air PCs are investigated by replacing steel cylinders for elliptical rods. At the same lattice constant and filling fraction, a novel low-frequency stop band occurs between the first and the second bands for elliptical scatters. And the width of the second lowest BG for elliptical scatters is as the same as the lowest BG for steel cylinders at appropriate filling fraction. According to these results, we design a tandem structure to open wide low-frequency band gap under decreasing space size.(4) Localization characteristic for steel/water PCs defect statesLocalization characteristic of several point and line defects are considered by the FEM and experiment. In the stop band frequency, acoustic wave is localized at these defects, and hence forms a resonantor or waveguide. Acoustic wave propagate along the line defect almost losslessly, but for a single point defect, the calculated transmission amplitude is very low at localized frequency. Eexperimental results of line defect are in accordance with numerical results, but for point defect, there exists a little shift for localized frequency between experimental and numerical results. Combining the localization characteristics of single point and line defects, a waveguide–cavity-waveguide structure is designed. Computed transmission spectra show that the transmission ratio of this structure is nearly to 100%, which improves the localization effect of single point defect mostly.(5) Discusses on intelligent PCsMagnetorheological elastomer (MRE) is introduced in PCs field. For solid/MRE PCs, tunable BG dependence on external magnet field is considered with the PWE method.