Fugen Wu

Large acoustic band gaps created by rotating square rods in two-dimensional periodic composites

Effects of orientations of square rods on the acoustic band gaps in two-dimensional periodic arrays of rigid solid rods embedded in air are studied. The acoustic band gaps will be opened and enlarged greatly by increasing the rotation angle. For any filling fraction F, the maximum acoustic band gaps appear at the same rotation angle θ = 45° for the cases of F≤0.50, otherwise they will appear at different limit values θc and the largest band gap is achieved at a filling fraction of about F = 0.85. This gap-tuning effect will be stronger with increase in filling fraction. This tuning mechanism of band gap suggests a new way to design band gaps of two-dimensional phononic crystals.

Numerical study of Lamb waves band structure in one-dimensional phononic crystal slabs with the anti-symmetric boundary structure

This paper theoretically and numerically investigates the propagation of Lamb waves in a one-dimensional phononic crystal slab bordered with anti-symmetric boundary layers. The results show that the band structure of the anti-symmetric boundary phononic crystal is significantly different from those presented in the papers available. The eigenmodes displacement fields reveal that there is an essential distinction in the formation of the band gap between the anti-symmetric and the symmetric boundary model. On the other hand, the thickness of the boundary layers can remarkably change the width and the location of the band gaps. Furthermore, the variation of the phononic crystal band gaps and the band pinning elimination show the band gaps are sensitive to the degree of stagger of the boundary layers, and different band gap has a different response to the profile of the boundary. In other words, the topological distribution of the boundary layer has an influence on the band structures.

Acoustic beam splitting in two-dimensional phononic crystals using self-collimation effect

We propose two models of self-collimation-based beam splitters in phononic crystals. The finite element method is used to investigate the propagation properties of acoustic waves in two-dimensional phononic crystals. The calculated results show that the efficiency of the beam splitter can be controlled systematically by varying the radius of the rods or by changing the orientation of the square rods in the line defect. The effect of changing the side length of the square rods on acoustic wave propagation is discussed. The results show that the total transmission/reflection range decreases/increases as the side length increases. We also find that the relationship between the orientation of the transflective point and the side length of the square rods is quasi-linear.

Thermal tuning of Lamb wave band structure in a two-dimensional phononic crystal plate

Using supercell-plane-wave-expansion method, we have made a theoretical study of the temperature effects on the band structure of Lamb wave in a two-dimensional phononic crystal plate. The numerical results show that the Lamb wave bandgap is very sensitive to temperature. For the case of Ba0.7Sr0.3TiO3/epoxy phononic crystal, the width of bandgap becomes narrower in a hexagonal lattice system as the temperature increases, but it becomes wider in a phononic crystal plate with square lattice. On the other hand, for the case of air/Ba0.7Sr0.3TiO3 plate with square lattice, wider and higher complete bandgap can be created in a higher temperature. These results are quite different from that in the infinite phononic crystal and one-dimensional phononic crystal plate.

Larger acoustic band gaps obtained by configurations of rods in two-dimensional phononic crystals

A method is introduced to optimize the acoustic band structures of two-dimensional phononic crystals (PCs). The acoustic band gap (ABG) between any two bands could be maximized by introducing an additional rod at a suitable position in a unit cell. The results also show that the symmetry reduction of the system is more efficient in creating the ABGs except for the first one. This additional rod method will be useful in designing the ABGs of PCs.

Effects of asymmetrical rotated rectangular basis on the acoustic band gap in two-dimensional acoustic crystals: the bands are twisted

The band structure and the change in band extremas position during the rotation of bases are analysed in two-dimensional rectangular-basis acoustic crystals (ACs) with a square lattice. We find that the bands of ACs are twisted and some of the extrema of the bands move anticlockwise or clockwise in the whole area of the first Brillouin zone (BZ) when the bases are rotated clockwise. These make the irreducible BZ expand into the whole first BZ. Therefore, for the ACs with a rectangular basis or similar kind of basis, it is important to study the whole first BZ to obtain the accurate band structure.

Point defect states in 2D acoustic band gap materials consisting of solid cylinders in viscous liquid

We investigated point defect states in two-dimensional acoustic band gap materials consisting of steel cylinders in liquid with viscous damping. Numerical results show that when the viscous penetration depth is comparable to the structural length scale, point defect states fall in large complete acoustic band gaps. It is also found that the magnitude of the viscosity in the liquid has an influence on the gap and defect state properties at the same time and that large viscous damping can enlarge the band gap but assemble the defect states. An expected gap frequency and a defect state frequency can be obtained by choosing a proper viscous damping parameter θ.

Tuning the acoustic directional radiation by rotating square rods in two-dimensional phononic crystals

Analysis is given to acoustic directional radiation tuned by rotating square rods in two-dimensional (2D) solid–fluid phononic crystals (PC). The contour line method is introduced which predicts how the acoustic waves propagate at different frequency. As a specific example, for the systems of steel rods with square cross-section in a water host, we employ this approach to the analysis of the directivity successfully. The directional radiation frequency of two lowest bands are studied in this paper. The results show that the directional radiation frequency can be turned in a wide range by rotating the square rods. While the directivity of acoustic propagation keeps unchanged when the acoustic directional radiation frequency is located in the same band. Moreover, PCs exhibit excellent characteristic of single radiation branch as a corner cut off in a finite structure. Our approach may supply a new way to tune the directional radiation frequency.

LOCALIZED MODES OF A COMPRESSION WAVE IN TWO-DIMENSIONAL SOLID–SOLID PHONONIC CRYSTALS

We have studied the compression (P) wave band structures at a low frequency in two-dimensional solid–solid phononic crystals. The plane-wave expansion method based on the decomposition of elastic waves was used. The pressure field distribution of P-wave localized modes at Γ points in the lowest bands, including multiple flat bands of systems comprising different configurations, were analyzed. The results show that a lower symmetry of the scatterer are an effective method to enhance the localization of vibration modes. The property has potential applications in the design of waveguides.

METHOD OF TUNING FREQUENCY OF THE DEFECT MODE IN TWO-DIMENSIONAL SQUARE PHOTONIC CRYSTALS

In this paper, we investigate the defect modes created by taking a single rod away from the center of the supercell in two-dimensional photonic crystals. Through theoretical calculation, we find that the defect band can exist in the photonic band gaps, and the position of the defect band frequency intensively depends on the position and radius size of the defect rod. When the radius of the defect rod is bigger than that of the normal rods, the frequency of the defect band can be tunable in a wider range by moving the defect position while the doubly degenerate defect modes may split into two nondegenerate defect modes. The investigation provides a theoretical instruction to design the optical resonator with tunable frequency.