Band Structures Of Phononic Crystals Research Articles

Using coupling slabs to tailor surface-acoustic-wave band structures in phononic crystals consisting of pillars attached to elastic substrates

The propagation of surface acoustic waves (SAWs) in two-dimensional phononic crystals (PnCs) with and without coupling-enhancement slabs was theoretically investigated using a three-dimensional finite element method. Different piezoelectric substrates, for example, lithium niobate (LiNbO3), gallium nitride (GaN), and aluminium nitride (AlN), were taken into account. Compared to the PnCs without coupling-enhancement slabs, the coupling between each pillar and its nearest neighbor was largely enhanced in the presence of slabs. The bandwidth of the first directional band gap increased markedly compared with its initial value for the PnCs without a slab (within square symmetry). In addition, with increasing thicknesses of the slabs bonded between neighboring pillars, the first directional band-gap and second directional band gap of the PnCs tend to merge. Therefore, the structure with coupling-enhancement slabs can be used as an excellent electrical band elimination filter for most electro-SAW devices, offering a new strategy to realize chip-scale applications in electroacoustic signal processing, optoacoustic modulation, and even SAW microfluidic devices.

The topological phase transition and the tunable interface states in granular crystal

Topological phase is a new degree of freedom to describe the state of matter in condensed matter physics. One could predict the existence of the interface state between two topological different phononic crystals. The band structures of phononic crystal depend on the characteristics of their composite and their combination, such as geometry, filling fraction, and stiffness. However, after the phononic crystal is fabricated out, it is relatively difficult to tune their band structure and its topology. In order to broaden the application scope of phononic crystals, different kinds of tunable phononic crystals have been proposed. One method to achieve this tunability is to introduce nonlinearity into the phononic crystals. Granular crystals is one type of tunable nonlinear material, whose nonlinearity stems from nonlinear Hertzian contact. By changing the static precompression, the dispersion of granular crystals can be tuned. In this paper, by combining topology with nonlinear we create a new type of interface state switch without changing the experimental setup. Based on the Su-Schrieffer-Heeger (SSH) model–an example of a one dimensional (1D) topological insulator, we present a 1D nonlinear granular crystal, to realize the topological transition by precompression. First, we construct a 1D mechanical structure, which is made up of nonlinear granular crystal and linear phononic crystal. The 1D nonlinear granular crystal is simplified as a “mass-spring” model with tunable elastic constant and invariable elastic constant. By calculating the band topology–the Zak phase, we found that the Zak phase of the two bands can switch from π to 0. There exist a critical precompression F0, when F F0 the Zak phase of the band is π, when F > F0 the Zak phase is 0. The granular crystal vary from nontrivial bandgap to trivial one as precompression gradually increase. This effect enables us to design interface state switch at the interface between granular crystals with trivial and nontrivial band gap. Furthermore, when F F0, we find that the localization of interface state decreases as the applied precompression increases. Thus, we investigate existence of the interface state under different precompression and found that the interface state can be controlled freely. We anticipate these results to enable the creation of novel tunable acoustic devices.

Accelerated Approach for the Band Structures Calculation of Phononic Crystals by Finite Element Method

We present here a fast and easily realized computational approach based on the finite element methods with consistent and lumped mass matrices (CM-FEM and LM-FEM, respectively), and the Bloch’s theorem, to calculate the elastic band structures of phononic crystals. Two improvements, the adjustment of the introduction of Bloch’s theorem as well as weighting treatment of consistent and lumped mass matrices, are performed. Numerical simulations show that convergence speed is accelerated obviously. Furthermore, the method is verified by analytical solutions in specified homogeneous cases. It is concluded that compared with CM-FEM or LM-FEM, the present method gives higher precision results with sparser mesh and takes less time.

Wave propagation in single column woodpile phononic crystals: Formation of tunable band gaps

We study the formation of frequency band gaps in single column woodpile phononic crystals composed of orthogonally stacked slender cylinders. We focus on investigating the effect of the cylinders׳ local vibrations on the dispersion of elastic waves along the stacking direction of the woodpile phononic crystals. We experimentally verify that their frequency band structures depend significantly on the bending resonant behavior of unit cells. We propose a simple theoretical model based on a discrete element method to associate the behavior of locally resonant cylindrical rods with the band gap formation mechanism in woodpile phononic crystals. The findings in this work imply that we can achieve versatile control of frequency band structures in phononic crystals by using woodpile architectures. The woodpile phononic crystals can form a new type of vibration filtering devices that offer an enhanced degree of freedom in manipulating stress wave propagation.

Bending vibration band structure of phononic crystal beam by modified transfer matrix method

The bending vibration band structure of phononic crystal (PC) beam is solved by a unified formulation of the modified transfer matrix (MTM) method in this paper. The improvement of MTM method is the introduction of constitutive matrix U and matrix of derivative functions V, which standardizes and simplifies the deduction by the matrix operation. The band structure of an epoxy-aluminum PC Timoshenko beam is calculated by both MTM method and plane wave expansion (PWE) method. The results show that the present MTM method has a great advantage in the precision of the result. In addition, the formulation of transfer matrix derived from Timoshenko beam condition is a general form which is also suitable for other general beam structures just by replacing corresponding matrices.

Tunable passband in one-dimensional phononic crystal containing a piezoelectric 0.62Pb(Mg1/3Nb2/3)O3–0.38PbTiO3 single crystal defect layer

Longitudinal acoustic wave propagation in one-dimensional phononic crystal containing a 0.2mol% Fe-doped relaxor-based ferroelectric 0.62Pb(Mg1/3Nb2/3)O3–0.38PbTiO3 (PMN–0.38PT) single crystal defect layer is theoretically studied using the transfer matrix method. A passband can be produced in the stopband when the inserted PMN–0.38PT layer with thickness around its half wavelength. The frequency of the passband is closely dependent on the PMN–PT strain coefficient, suggesting that the band structure of phononic crystal is tunable by applying external electric field onto the piezoelectric crystal. Also, we investigated the influence of acoustic impedance of periodic constitutive materials (layers A and B) on the passband, where the bandwidth of the new passband becomes narrower as the acoustic impedance ratio of layer A and B (ZA/ZB) increase. The simulated results provide valuable guidance for designing tunable acoustic filters and switches made of phononic crystal consisting of the piezoelectric defect layer.

Band gap tunability of magneto-elastic phononic crystal

The possibility of control and tuning of the band structures of phononic crystals offered by the introduction of an active magnetoelastic material and the application of an external magnetic field is studied. Two means to obtain large elastic properties variations in magnetoelastic material are considered: Giant magnetostriction and spin reorientation transition effects. A plane wave expansion method is used to calculate the band structures. The magnetoelastic coupling is taken into account through the consideration of an equivalent piezomagnetic material model with elastic, piezomagnetic, and magnetic permeability tensors varying as a function of the amplitude and orientation of the applied magnetic field. Results of contactless tunability of the absolute bandgap are presented for a two-dimensional phononic crystal constituted of Terfenol-D square rod embedded in an epoxy matrix.

Band structure in two-dimensional fiber–air phononic crystals

A two-dimensional phononic crystal (PC) composed of textile fiber and air is initially discussed in this paper, which is different from the previous PCs with rigid inclusions. The plain wave expansion method is used to calculate band structure of different PCs by altering fiber material properties and structure parameters. Numerical results show that the effect of material properties of soft fiber on band structure of phononic crystal can be ignored, while the effect of structural parameters is obvious.

Band structure of phononic crystals with general damping

In this paper, we present theoretical formalisms for the study of wave dispersion in damped elastic periodic materials. We adopt the well known structural dynamics techniques of modal analysis and state-space transformation and formulate them for the Bloch wave propagation problem. First, we consider a one-dimensional lumped parameter model of a phononic crystal consisting of two masses in the unit cell whereby the masses are connected by springs and dashpot viscous dampers. We then extend our analysis to the study of a two-dimensional phononic crystal, modeled as a dissipative elastic continuum, and consisting of a periodic arrangement of square inclusions distributed in a matrix base material. For our damping model, we consider both proportional damping and general damping. Our results demonstrate the effects of damping on the frequency band structure for various types and levels of damping. In particular, we reveal two intriguing phenomena: branch overtaking and branch cut-off. The former may result in an abrupt drop in the relative band gap size, and the latter implies an opening of full or partial wavenumber (wave vector) band gaps. Following our frequency band structure analysis, we illustrate the concept of a damping ratio band structure.

Existence of complete band gaps in 2D steel-water phononic crystal with square lattice

This paper theoretically and experimentally studies the existence of complete band gaps in two-dimensional (2D) phononic crystal consisting of parallel steel rods in water with square lattice. The band structure of phononic crystal is calculated by a plane wave expansion (PWE) method. Based on the well-known ultrasonic immersion transmission technique, the overlapping transmission spectra of acoustic waves, a complete band gap, is experimentally measured along the two high-symmetry directions of the first irreducible Brillouin zone. There is a very good agreement between the experimental result and the range of frequencies of the complete band gap.

Tunable magnetoelastic phononic crystals

The feasibility of tuning the band structure of phononic crystals is demonstrated by employing magnetostrictive materials and applying an external magnetic field. Band structures are calculated with a plane wave expansion method that accounts for coupling between the elastic behavior and the magnetic field through the development of elastic, piezomagnetic, and magnetic permeability effective tensors. We show the contactless tunability of the absolute band gaps of a two-dimensional phononic crystal composed of an epoxy matrix and Terfenol-D inclusions. The tunable phononic crystal behaves like a transmission switch for elastic waves when the magnitude of an applied magnetic field crosses a threshold.

Evanescent Bloch waves and the complex band structure of phononic crystals

The complex band structure of a phononic crystal is composed of both propagating and evanescent Bloch waves. Evanescent Bloch waves are involved in the diffraction of acoustic phonons at the interfaces of finite phononic crystal structures. They are shown to arise both because of band gaps, where they directly measure the exponential decrease upon transmission, and because of the frustrated nature of higher-order diffracted waves at low frequencies. These diffracted evanescent Bloch waves become propagative as the frequency increases thus populating higher frequency bands. These results should apply as well to any periodic medium supporting the propagation of waves.

Negative Refraction of Acoustic Waves in a Two-Dimensional Phononic Crystal via FDTD Simulation

Negative refraction of acoustic waves in a two-dimensional (2D) phononic crystal is studied by numerical simulation based on the finite-difference time-domain (FDTD) method. We calculate the phonon band structure of 2D phononic crystals, consisting of metal cylinders placed periodically in a liquid. By comparing several combinations of materials for metal cylinder and liquid, we analyze the dependence of the band structures on sound speed and density of liquid media. The negative refraction of the acoustic waves is observed at the interfaces between the phononic crystal slab and the liquid. We find that an acoustic “lens effect” with the slab appears due to the negative refractions. The relationship between the focal intensity in the lens effect and the band structure of the phononic crystal is quantitatively discussed.

The influence of pore shapes on the band structures in phononic crystals with periodic distributed void pores

The influence of the pore shapes on the band structures in phononic crystals with periodic distributed void pores are investigated in this paper. By using finite difference time domain (FDTD) scheme, the dispersion properties of the in-plane x– y mode waves in the materials with triangular, circular or square pores are discussed respectively. The influence of the pore shapes and the porosity on the band gap structures is analyzed. The results show that for x– y mode waves, the stop bands are easily formed in the materials with triangular pores, but hard for square ones. Moreover, a critical porosity exists for the formation of the absolute band gaps. Along with the increase of the porosity, the width of the absolute band gap is increased, but the centre frequency is dropped.

Phononic band gaps of elastic periodic structures: A homogenization theory study

In this study, we investigate the band structures of phononic crystals with particular emphasis on the effects of the mass density ratio and of the contrast of elastic constants. The phononic crystals consist of arrays of different media embedded in a rubber or epoxy. It is shown that the density ratio rather than the contrast of elastic constants is the dominant factor that opens up phononic band gaps. The physical background of this observation is explained by applying the theory of homogenization to investigate the group velocities of the low-frequency bands at the center of symmetry $\ensuremath{\Gamma}$.

Lumped-mass method for the study of band structure in two-dimensional phononic crystals

A lumped-mass method is introduced to study the propagation of elastic waves in two-dimensional periodic systems. First, it is used to calculate the band structure of an array of Pb columns in an epoxy background. Second, the method is applied to the same array of Pb columns in a soft rubber background. The results are compared with those calculated with the well-known plane-wave expansion formalism, where the advantages of the lumped-mass method are pointed out and analyzed. These advantages make it possible for easy calculations of band structures of phononic crystals with interfaces of large contrast of elastic constants as well as units of any shapes.

A study of the band structure in two-dimensional phononic crystals based on plane-wave algorithm

In this paper, the calculating course of the plane-wave algorithm is introducedto solve the sound wave equation and the band structure of phononic crystals. The phononic crystals of two-dimensional binary liquid systems are studied. In conclusion, the CCl4/mercury system is easier to obtain the band-gap than the mercury/CCl4 system. With the increase of the filling fraction(f), the width of the band-gap becomes wider and then narrower. The widest band-gap of CCl4/mercury system appears at f=0229,where ΔΩmax=0549.While the width of the band-gap in mercury/CCl4 system increases consistently with the filling fraction, when f=0.554,ΔΩmax=0515.Under the same filling fraction, the variation of the cylinder diameter and lattice constant does not affect the band-gap width ΔΩ.