Two-dimensional Phononic Crystal Plate Research Articles

Acoustic manipulation of microparticles using a two-dimensional phononic crystal plate

Acoustic waves can manipulate particles without contact or damage, and has received increasing attention due to their potential applications in various fields, such as cell sorting, organoid construction, and material assembly. In general, high-throughput manipulation of microparticles relies on a large number of active transducers and phase-shifting circuits to create standing wave patterns, thus significantly inducing system complexity. Recently, we realized the parallel manipulation of microparticles by using an acoustic field modulated by a one-dimensional phononic crystal plate. The concept is based on the fact that phononic crystal plate can resonantly excite the zero-order asymmetric (<i>A</i><sub>0</sub>) Lamb wave, inducing highly localized periodic radiation force on the particles. In this paper, we further show that by using a two-dimensional phononic crystal plate (TDPCP), parallel manipulation of massive particles can be achieved only with a single transducer. The <i>A</i><sub>0</sub> Lamb wave can be excited by a TDPCP, forming a two-dimensional periodic localized field, and then particles can suffer negative vertical force and stable zero horizontal force, inducing two-dimensional periodic trapping on the surface of the plate. Combining a PZT source with a TDPCP consisting of a brass plate patterned with periodical brass stubs, we observe the capture and arrangement of glass microspheres, achieving two-dimensional arrangement manipulation of particles on the TDPCP. This system represents a significant advancement in developing high-throughput, rapid, and flexible devices for particles and cell manipulation.

Tunable low-frequency bandgaps of a new two-dimensional multi-component phononic crystal under different pressures, geometric parameters and pre-compression strains

For the control of low-frequency noise in complex external-pressure environment, a new two-dimensional phononic crystal plate which is made of the lead stub with rubber coatings connected by narrow epoxy bars is proposed and the bandgap characteristics are simulated tentatively by the finite element method. The bandgap generation mechanism of the designed model is investigated by analyzing corresponding vibration modes. Furthermore, the bandgap adjustability under different pre-compression strains and geometric parameters is also investigated. Results show that obvious bandgaps tunability with small pre-compression strains or hydrostatic pressure is realized by changing geometric parameters and applying pre-compression strain to the matrix.

Type-II Dirac points and edge transports in phononic crystal plates

The accidentally degenerate type-II Dirac points in sonic crystal has been realized recently. However, elastic phononic crystals with type-II Dirac points have not yet been explored. In this work, we design a two-dimensional phononic crystal plate in square lattice with type-II Dirac points for elastic waves. The type-II Dirac points, different from the type-I counterparts, have the tiled dispersions and thus the iso-frequency contours become crossed lines. By tuning structures to break the mirror symmetry, the degeneracies of the type-II Dirac points are lifted, leading to a band inversion. In order to have a further explanation, we also calculate the Berry curvatures of phononic crystals with opposite structure parameters, and it turns out that these two crystals hold opposite signs around the valley. The phononic crystal plates before and after the band inversion belong to different topological valley phases, whose direct consequence is that the topologically protected gapless interface states exist between two distinct topological phases. Topologically protected interface states are found by calculating the projected band structures of a supercell that contains two kinds of interfaces between two topological phases. Robustness of the interface transport is verified by comparing the transmission rate for perfect interface with that for defective interface. Moreover, owing to the special stress field distributions of the elastic plate waves, the boundaries of a single phononic crystal phase can similarly host the gapless boundary states, which is found by calculating the projected band structures of a supercell with a single phase, thus having two free boundaries on the edges. This paper extends the two-dimensional Dirac points and valley states in graphene-like systems to the type-II cases, and obtains in the same structure the gapless interface and boundary propagations. Owing to the simple design scheme of the structure, the phononic crystal plates can be fabricated and scaled to a small size. Our system provides a feasible way of constructing high-frequency elastic wave devices.

Low-frequency bandgaps of two-dimensional phononic crystal plate composed of asymmetric double-sided cylinder stubs

In this paper, we theoretically investigate the propagation characteristics of Lamb wave in a two-dimensional (2D) asymmetric phononic crystal (PC) plate composed of cylinder stubs of different radius deposited on both sides of a thin homogeneous plate. The dispersion relations, transmission spectra and displacement fields of the eigenmodes are calculated by using the finite element method (FEM). Two complete bandgaps (BGs) can be found in low-frequency range and the transmission spectra coincide with the band structures. We investigate the evolution of dispersion relations with the decrease of the upper stub radius. The physical mechanism of the upper stub radius effect is also studied with the displacement fields of the unit cell. Numerical results show that the symmetry of the stub radius can remarkably influence the band structures and the asymmetric double-sided plate exhibits a new bandgap (BG) in lower frequency range due to the coupling between the lower stub’s resonant mode and the plate’s Lamb mode becomes weak and the adjacent bands separate. Moreover, we further investigate the effect of the stub height on the dispersion relations and find that the BGs shift to lower frequency regions with the increase of the stub height. In addition, the BGs’ sensitivity to the upper stub radius and the stub height is discussed. The low-frequency BGs in the proposed PC plate can potentially be used to control and insulate vibration in low frequency range.

Extending and lowing band gaps in one-dimensional phononic crystal strip with pillars and holes

Effectiveness of extending and lowing gaps in one-dimensional phononic crystal strips is conducted by periodically patterning pillar-type strip with holes. Finite element method is applied to the hybrid unit to calculate band structures and eigen modes. Transmission spectra and displacement fields are investigated to confirm the gap effect in the studied hybrid strips. Numerical results show that, the one-dimensional hybrid strip can open lower and wider gaps. Compared with two-dimensional phononic crystal plate, band structures of phononic crystal strip show different group velocities and frequencies in low-order bands, different eigen modes of gap edge because of boundary condition difference. The effectiveness of modulating gaps with strip width is investigated. Gap degeneration happens to adjust lower gap edge downward. Besides, hybrid structure with double-side pillar leads to more resonance bands than that with single-side pillar. Vibration mode of pure pillar type structure located in lower edge of the gap of hybrid single-side pillar-type structure, and some resonance modes in the hole-type strip are reserved in hybrid single-side pillar structure. Resonance in hybrid double-side pillar structure is introduced by vibration of the double-pillar character, to create more flat bands. Furthermore, gap sensitivity to geometrical parameters of pillars and holes is also investigated.

Edge waves and resonances in two-dimensional phononic crystal plates

We present a numerical study on phononic band gaps and resonances occurring at the edge of a semi-infinite two-dimensional (2D) phononic crystal plate. The edge supports localized edge waves coupling to evanescent phononic plate modes that decay exponentially into the semi-infinite phononic crystal plate. The band-gap range and the number of edge-wave eigenmodes can be tailored by tuning the distance between the edge and the semi-infinite 2D phononic lattice. As a result, a phononic band gap for simultaneous edge waves and plate waves is created, and phononic cavities beside the edge can be built to support high-frequency edge resonances. We design an L3 edge cavity and analyze its resonance characteristics. Based on the band gap, high quality factor and strong confinement of resonant edge modes are achieved. The results enable enhanced control over acoustic energy flow in phononic crystal plates, which can be used in designing micro and nanoscale resonant devices and coupling of edge resonances to other types of phononic or photonic crystal cavities.

Interface-guided mode of Lamb waves in a two-dimensional phononic crystal plate**Project supported by the National Natural Science Foundation of China (Grant Nos. 11374068 and 11374066), the Science & Technology Star of Zhujiang Foundation of Guangzhou, China (Grant No. 2011J2200013), and the Natural Science Foundation of Guangdong, China (Grant No. S2012020010885).

We investigate the interface-guided mode of Lamb waves in a phononic crystal heterostructures plate, which is composed of two different semi-infinite phononic crystal (PC) plates. The interface-guided modes of the Lamb wave can be obtained by the lateral lattice slipping or by the interface longitudinal gliding. Significantly, it is observed that the condition to generate the interface-guided modes of the Lamb wave is more demanding than that of the studied fluid–fluid system. The interface-guided modes are strongly affected not only by the relative movement of the two semi-infinite PCs but also by the thickness of the PC plate.

Laser-Ultrasonic Investigation on Lamb Waves in Two-Dimensional Phononic Crystal Plates

In this paper, laser-ultrasonic non-destructive testing is used to investigate the propagation of Lamb waves in two-dimensional phononic crystal plates. The bandgaps are experimentally observed for low-order Lamb wave modes. The influence of crucial parameters such as the periodical arrangement of scatterers on bandgaps is discussed in detail. The finite element simulations further agree well with the results of the laser-ultrasonic investigation.

Band gaps in the low-frequency range based on the two-dimensional phononic crystal plates composed of rubber matrix with periodic steel stubs

In this paper, the numerical investigation of elastic wave propagation in two-dimensional phononic crystals composed of an array of steel stepped resonators on a thin rubber slab is presented. For the first time the rubber material is used as the matrix of the PCs. With the finite-element method, the dispersion relations of this novel PCs structure and some factors of the band structure are studied. Results show that, with the rubber material as matrix, the PC structures exhibit extremely low-frequency band gaps, in the frequency range of hundreds of Hz or even tens of Hz; the geometrical parameters and the material parameters can modulate the band gaps to different extents. Furthermore, to understand the low-frequency band gaps caused by this new structure, some resonance eigenmodes of the structure are calculated. Results show that the vibration of the unit cell of the structure can be seen as several mass–spring systems, in which the vibration of the steel stepped resonator decides the lower boundary of the first band gap and the vibration of the rubber that is not in contact with the resonator decides the upper boundary.

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.

The investigation of point defect modes of phononic crystal for high Q resonance

Point defect cavity was constructed in a two-dimensional phononic crystal plate. It was excited by a small piezo chip in the cavity, and the vibrations of each point defect mode were detected by an optical interferometer. Point defect modes on 2D phononic crystal plate in vacuum, air, and with water loaded were investigated theoretically and experimentally. It is shown that the Q factors of the point defect modes are determined by inner attenuation, bandgap effects, and medium. The SSS mode (breathing mode) has highest Q factor in vacuum and air among nine modes thanks to low inner attenuation and low energy leakage. By selectively loading the PC with water on one side, the point defect modes with shear movement surfaces suffer lower attenuation and still have rather high Q factors. These conclusions will help to design a new kind of resonator or sensor.

Lamb waves in two-dimensional phononic crystal plate with anisotropic inclusions

An analysis is given to the band structure of the two-dimensional phononic crystal plate constituted of a square array of elastic anisotropic, circular Pb cylinders embedded in elastic isotropic epoxy. The numerical results show that the band gap can be tuned by rotating the anisotropic material orientation. It is found that the influence of anisotropy on band gap of Lamb wave is clearly different from that on the band gap of bulk waves. The thickness of the system under study is a sensitive parameter to affect the influence of anisotropic materials on the normalized gap width.

Symmetric and Anti-Symmetric Lamb Waves in a Two-Dimensional Phononic Crystal Plate

It is well known that Lamb waves in a plate with a mirror plane can be separated into two uncoupled sets: symmetric and anti-symmetric modes. Based on this property, we present a revised plane wave expansion method (PWE) to calculate the band structure of a phononic crystal (PC) plate with a mirror plane. The developed PWE method can be used to calculate the band structure of symmetric and anti-symmetric modes separately, by which the depending relationship between the partial acoustic band gap (PABG), which belongs to the symmetric and anti-symmetric modes alternatively, and the position of the scatterers can be determined. As an example of its application, the band structure of the Lamb modes in a two-dimensional PC plate with two layers of void circular inclusions is investigated. The results show that the band structure for the symmetric and anti-symmetric modes can be changed by the position of the scatterers drastically, and larger PABGs will be opened when the scatterers are inserted into the area of the plate, where the elastic potential energy is concentrated.

Absolute forbidden bands and waveguiding in two-dimensional phononic crystal plates

We introduce a supercell plane wave expansion (SC-PWE) method for the calculation of elastic band structures of two-dimensional phononic crystal plates. We compute the band structure of solid-solid and air-solid two-dimensional phononic crystal plates. The air is modeled as a low impedance medium (LIM) with very low density and very high velocities of sound. We investigate the influence of the constituent materials, of the plate thickness, and of the geometry of the array on the band structure. We establish the range of validity of the SC-PWE method in terms of the rate of convergence with respect to the number of plane waves and contrast in physical properties of the matrix and inclusion materials. We show that for high contrast solid-solid phononic crystal plates, our SC-PWE method, as other PWE-based methods introduced to date, suffers from convergence difficulties. In the case of air (modeled as the LIM) holes-solid plates, we demonstrate that the SC-PWE method leads to fast convergence for a wide range of values of solid physical properties. With these constituent materials, we find that the largest absolute forbidden bands occur in the band structure of the phononic crystal plate provided the thickness of the plate is of the order of magnitude of the periodicity of the array of inclusions. We demonstrate the existence of guided modes in an air-silicon phononic crystal plate containing a linear defect.

Propagation of Lamb Waves in Phononic-Crystal Plates

AbstractIn this paper, the band structures of Lamb waves in the two-dimensional phononic-crystal plates are calculated and analyzed based on the plane wave expansion method. The phononic-crystal plates are composed of an array of circular crystalline iron cylinders embedded in the epoxy matrix. Square lattice and triangular lattice are analyzed and discussed, respectively. For the square lattice, two complete band gaps exist, and a narrow pass band between the complete band gaps separates them apart. For the triangular lattice, a wide complete band gap existing with the ratio of gap width to midgap frequency Δω/ωm equal to 72% is found. Furthermore, the influence of the plate thickness is crucial for band structures of Lamb waves. Tuning plate thickness can shift the pass bands effectively, and band shifting causes the variation of the width of complete band gap and its opening and closure.