Phononic Crystal Plate Research Articles

Defect states and vibration energy recovery of novel two-dimensional piezoelectric phononic crystal plate

The band structure and transmission characteristics of a new two-dimensional (2D) piezoelectric phononic crystal plate consisting of four epoxy short plates periodically connected with a square lattice of a prismatic piezoelectric material coated with plexiglass are investigated by supercell method and finite element method. By changing the electric boundary conditions imposed on the upper and lower surfaces of piezoelectric scatterers, a point defect waveguide with adjustable paths is formed, which overcomes the limitation of immutability in the direction of the vibration waveguide, with material and structural parameters fixed. Then the controlling of the piezoelectric effect can change the material parameters of piezoelectric components in phononic crystals, showing that the piezoelectric constants have a great influence on the complete bandgap, which is beneficial to the formation of defect states; when the frequency of the defect state appears in the band gap, the frequency-responding range of the defect state expands. The analysis of the displacement vector field indicates that the strain energy in the resonance of the new structure is almost completely limited to the upper and lower surfaces of the central piezoelectric scatterer. We use the recycling circuit to connect the electrodes on the upper and lower surfaces of the piezoelectric sheet. At this time, the output electrical energy can supply the power to the DC load, and the mechanical energy of vibration can be converted into electrical energy. The results of this work provide a reference for the self-powered technology of waveguide and wireless sensor device with adjustable path.

Tunable bandgaps in soft phononic plates with spring-mass-like resonators

Controlling band gaps of phononic crystals in real time through external stimuli (e.g. mechanical loadings, electric fields, and magnetic fields) shows potential applications in adaptive acoustic devices. It has been indicated that alteration of structural geometry or effective material properties due to external mechanical loadings will effectively change the bandgaps. In this regard, inducing significant post-buckling deformations in phononic crystals becomes an effective way to tune the band gaps. Few studies however have been reported to tune the band gaps through small deformations under which the geometry of phononic crystals is almost unchanged. In this work, a phononic crystal plate made of soft material with resonant units is proposed. Each resonant unit consists of a mass which is connected to the perforated plate by thin beams. Finite element method is employed to study the deformation and the dispersion behavior of such structure when subject to external mechanical loadings. Obvious complete band gaps are found to even exist in the intact structure without any mechanical loading. The evolution of band gaps under stretching is systematically revealed. Results show that remarkable tunability of bandgaps with small pre-stretch or extension is realized when strong resonance appears for some particular modes. The resonance frequency is mainly affected by the mass of the resonator and the stiffness of the connecting beams. In the proposed structure, the stiffness of the connecting beams can be substantially increased under a small pre-stretch. As a result, the resonance frequencies of resonant modes are increased, giving rise to a remarkable modification of the band gaps, while the geometry of the structure is nearly unchanged.

Simulation and experimental investigation of low-frequency vibration reduction of honeycomb phononic crystals**Project supported by the Fundamental Research Funds for the Central Universities, China (Grant No. NS2017003).

The honeycomb phononic crystal displays good performance in reducing vibration, especially at low frequency, but there are few corresponding experiments involving this kind of phononic crystal and the influence of geometric parameters on the bandgap is unclear. We design a honeycomb phononic crystal, which is assembled by using a chemigum plate and a steel column, calculate the bandgaps of the phononic crystal, and analyze the vibration modes. In the experiment, we attach a same-sized rubber plate and a phononic crystal to a steel plate separately in order to compare their vibration reduction performances. We use 8 × 8 unit cells as a complete phononic crystal plate to imitate an infinite period structure and choose a string suspension arrangement to support the experiment. The results show that the honeycomb phononic crystal can reduce the vibrating plate magnitude by up to 60 dB in a frequency range of 600 Hz–900 Hz, while the rubber plate can reduce only about 20 dB. In addition, we study the effect of the thickness of plate and the height and the radius of the column in order to choose the most superior parameters to achieve low frequency and wide bandgap.

Rapid acoustophoretic motion of microparticles manipulated by phononic crystals

We present the acoustophoretic motion of microparticles simultaneously driven by the acoustic streaming induced drag force (ASF) and acoustic radiation force (ARF) on a phononic crystal plate (PCP). A much faster acoustophoresis can be achieved via a PCP than a traditional standing wave in bulk and surface acoustic wave devices. The mechanism is attributed to the significantly enhanced ASF and ARF originating from the resonant excitation of a nonleaky zero-order antisymmetric Lamb mode intrinsically in the plate, which generates the highly localized field vertical to the surface and periodic field parallel to the surface. We also demonstrate the transition from the ASF dominated acoustophoresis to ARF dominated acoustophoresis as a function of particle size. The predicted trajectories and velocity of acoustophoretic particles by the proposed finite element model are in reasonable agreement with experimental phenomena. This study would aid the development of simple, scalable, integrated, and disposable phononic crystal based acoustofluidic systems for biomedical applications such as rapid mixing, cell trapping, sorting, and patterning.

Hybrid radial plate-type elastic metamaterials for lowering and widening acoustic bandgaps

In this paper, we present theoretical investigation on the wave propagation and acoustic bandgap characteristics in hybrid radial plate-type elastic metamaterials constituted of periodic double-sides composite stubs deposited on one-dimensional binary radial phononic crystal plate. The dispersion relations and the displacement fields of the eigenmodes are calculated by using the finite element method on the basis of two-dimensional axial symmetry models. Numerical results show that the proposed hybrid radial plate-type elastic metamaterial can generate lowering and widening acoustic bandgaps and yield a significant expansion of the relative bandwidth by a factor of 5 compared to the traditional radial plate-type elastic metamaterial with double-sided composite stubs. The displacement fields of the eigenmodes are applied to reveal the formation mechanism of lowering and widening acoustic bandgaps. In addition, the influences of the physical and geometrical parameters on the bandgaps are further performed. These low-frequency broadband acoustic bandgap properties in the radial plate-type elastic metamaterials can probably be applied to vibration and noise reduction in the rotary machines and structures.

Design of phononic crystals plate and application in vehicle sound insulation

The sound insulation performance of plates obviously affects the noise inside vehicle. Phononic crystals are periodic structures composed of various elastic materials. In this paper, the sound insulation performance of commonly used phononic crystals plates are analyzed by FEM (Finite Element Method), and some relevant conclusions are obtained. Based on the common two-dimensional convex phononic crystals, combined with micro perforated plate, a new type of phononic crystals plate is proposed, and the new combined phononic crystals structure is applied to the front plate of some automobile. The analysis results show that the combined phononic crystals plate has obvious effect on the noise reduction of the cab.

Robustness of conventional and topologically protected edge states in phononic crystal plates

In this work we theoretically study the interface acoustic states of resonators on a thin plate with topologically protected and conventional designs. Topologically protected interface state is first analyzed by employing the conception of breaking inversion symmetry within the unit cell of a honeycomb lattice for cylindrical and spherical resonators; we further demonstrate the robustness of the wave propagation along a zig-zag path containing sharp corners, defect and disorder. The wave propagation ceases to be preserved if we increase the degree of disorder along the zig-zag path. In parallel, the conventional interface state is also designed and compared to the same situations. We found that the conventional interface state suffers back scattering in the zig-zag path while it can show a more confined wave transport in some cases. The presence of a defect along the propagation path scatters the conventional interface wave and in particular can prohibit a full propagation in presence of a localized state at the defect. If the zig-zag path is made disordered, the propagation of the conventional interface mode can be conserved at given frequencies for a low random degree and disappears for higher random degree as the interface bands become flat in dispersion and turn to localized states. Finally, we show that the immunity of the topologically protected design needs the interface to be surrounded by at least two hexagons of the phononic crystals on both sides, especially at the sharp corners in the zig-zag path, while the conventional design only needs one hexagon bulk media with the advantage of compact wave transport. This work puts a step forward for the interface states in micro-/nano-scale characterization and figures out the behaviors for both topologically protected and conventional interface states.

Phononic crystal-enhanced near-boundary streaming for sonoporation

Efficient and controllable gene/drug delivery triggered by sonoporation is critical to cellular therapy. This study reports on repairable sonoporation for massive cells trapped on a phononic crystal plate (PCP). This mechanism is generated by the effects of enhanced near-boundary streaming around the manipulated cells. The streaming is achieved by significantly improving the tangential acoustic field gradient along the cell boundary through resonant PCP excitation of the nonleaky Lamb modes intrinsically existing in the uniform plate. This structured field-induced repairable sonoporation may constitute an effective tool for drug delivery and gene transfection.

Introducing Obliquely Perforated Phononic Plates for Enhanced Bandgap Efficiency.

Porous phononic crystal plates (PhPs) that are produced by perpendicular perforation of a uniform plate have well-known characteristics in selective manipulation (filtration, resonation, and steering) of guided wave modes. This paper introduces novel designs of porous PhPs made by an oblique perforation angle. Such obliquely perforated PhPs (OPhPs) have a non-uniform through-the-thickness cross section, which strongly affects their interaction with various wave mode types and therefore their corresponding phononic properties. Modal band analysis is performed in unit-cell scale and variation of phononic bandgaps with respect to the perforation angle is studied within the first 10 modal branches. Unit-cells with arbitrary perforation profile as well as unit-cells with optimized topology for maximized bandgap of fundamental modes are investigated. It is observed that the oblique perforation has promising effects in enhancing the unidirectional and/or omnidirectional bandgap efficiency, depending on the topology and perforation angle of OPhP.

A novel metal-matrix phononic crystal with a low-frequency, broad and complete, locally-resonant band gap

In this paper, a novel metal-matrix phononic crystal with a low-frequency, broad and complete, locally-resonant band gap, which includes the in-plane and out-of-plane band gaps, is investigated numerically. The proposed structure consists of double-sided single “hard” cylinder stubs, which are deposited on a two-dimensional locally-resonant phononic-crystal plate that consists of an array of rubber fillers embedded in a steel plate. Our results indicate that both the out-of-plane band gap and the in-plane band gap increase after introducing single “hard” cylinder stubs. More specifically, the out-of-plane band gap is increased by the out-of-plane analogous-rigid mode, while the in-plane band gap is increased by the in-plane analogous-rigid mode. The out-of-plane and the in-plane analogous-rigid mode are formed after introduction of the single “hard” cylinder stub. As a result, a broad, complete locally-resonant band gap in the low frequency is obtained due to the broad in-plane and out-of-plane band gaps overlapping. Compared to the classical double-sided stubbed metal-matrix phononic-crystal plate, the absolute bandwidth of the complete band gap is increased by a factor of 4.76 in the proposed structure. Furthermore, the effect of simple “hard” stubs on complete band gaps is investigated. The results show that the location of the complete band gaps can be modulated using a low frequency, and the bandwidth can be extended to a larger frequency range using different “hard” stubs. The new structure provides an effective way for metal-matrix phononic crystals to obtain broad and complete locally-resonant band gaps in the low-frequency range, which has many applications for low-frequency vibration reduction.

Acoustic manipulating of capsule-shaped particle assisted by phononic crystal plate

In this work, we present theoretical analyses of the acoustic radiation force acting on non-spherical particles, as well as experimental demonstration of particle trapping assisted by the artificially engineered acoustic field of the phononic crystal plate. The capsule-shaped particles, a kind of common non-spherical-shaped particles, in practical cases, are chosen as study objects. The dependence of the acoustic radiation force on different parameters such as the frequency, position, and orientation of a capsule-shaped particle is evaluated, and the analysis shows the orientation angle also has a great influence, which is quite different from the spherical particles. Due to the extraordinary resonant transmission of the phononic crystal plate, the periodically distributed acoustic field is obtained to realize trapping on capsule-shaped particle(s). This method could be envisaged to pave a way of delivering drugs or cells and small fibers in biology and medicine.

The Lamb wave bandgap variation of a locally resonant phononic crystal subjected to thermal deformation

A study on dynamical characteristics of a ternary locally resonant phononic crystal (PC) plate (i.e., hard scatterer with soft coating periodically disperse in stiff host matrix) is carried out in this paper. The effect of thermal deformation on the structure stiffness, which plays an important role in the PC’s dynamical characteristics, is considered. Results show that both the start and the stop frequency of bandgap shift to higher range with the thermal deformation. In particular, the characteristics of band structure change suddenly at critical buckling temperature. The effect of thermal deformation could be utilized for tuning of phononic band structures, which can promote their design and further applications.

Topological valley-chiral edge states of Lamb waves in elastic thin plates

We investigate the nontrivial topology of the band structure of Lamb waves in a thin phononic crystal plate. When inversion symmetry is broken, a valley pseudospin degree of freedom is formed around K and K′ valleys for the A0 Lamb mode, which is decoupled from the S0 and SH0 modes in the low-frequency regime. Chiral edge states are explicitly demonstrated, which are immune to defects and exhibit unidirectional transport behaviors when intervalley scattering is weak. The quantum valley Hall effect is thus simulated in a simple way in the context of Lamb waves.

Hybridization bandgap induced by an electrical resonance in piezoelectric metamaterial plates

We demonstrate numerically and experimentally the opening of a locally resonant bandgap in an active phononic crystal (PC) made of a homogeneous piezoelectric plate covered by a 1D periodic array of thin electrodes connected to inductive shunts. The application of periodic electrical boundary conditions (EBCs) enables an at will tailoring of the dispersion properties of the PC plate, thus leading to a control of the dispersion of the propagating guided elastic waves in the plate. Depending on the nature of the EBCs, several bandgaps open up, the most important being a Hybridization Bandgap (HBG) in the subwavelength regime. The PC behaves as a locally resonant metamaterial. The HBG originates from the interaction of propagating elastic waves (Lamb modes) with an electrical resonant mode whose dispersion can be effectively described through an equivalent transmission line model.

Selective Band Gap to Suppress the Spurious Acoustic Mode in Film Bulk Acoustic Resonator Structures

In this work, we investigate numerically the propagation of Lamb waves in a film bulk acoustic resonator (FBAR) structure formed by piezoelectric ZnO layer sandwiched between two Mo electrodes coupled with Bragg reflectors; the system is thus considered as a phononic-crystal (PnC) plate. The aim is to suppress the first-order symmetric Lamb wave mode considered as a spurious mode caused by the establishment of a lateral standing wave due to the reflection at the embedded lateral extremities of the structure; this spurious mode is superposing to the main longitudinal mode resonance of the FBAR. The finite element study, using harmonic and eigen-frequency analyses, is performed on the section of FBAR structure coupled with the PnC. In the presence of PnC, the simulation results show the evidence of a selective band gap where the parasitic mode is prohibited. The quality factor of the FBAR is enhanced by the introduction of the PnC. Indeed, the resonance and antiresonance frequencies passed from 1000 and 980 (without PnC) to 2350 and 1230 (with PnC), respectively. This is accompanied by a decrease in the electromechanical coupling coefficient from 10.60% to 6.61%.

The bandgap controlling by geometrical symmetry design in hybrid phononic crystal

The effects of symmetries on the bandgap in a newly designed hybrid phononic crystal plate composed of rubber slab and epoxy resin stub are studied for better controlling of bandgaps. The point group symmetry is changed by changing the orientation of the stub. The translation group symmetry is changed by changing the side length and the height of adjacent stubs. Results show that the point group symmetry and translation group symmetry can be important factors for controlling of the bandgaps of phononic crystal. Wider bandgap is obtained by suitable orientation of the stub. Lower bandgap appears when the differences between the adjacent stubs become bigger in supercell.

Bandgap properties in simplified model of composite locally resonant phononic crystal plate

This paper extends the traditional plane wave expansion (PWE) method to calculate the band structure of the proposed simplified model of composite locally resonant phononic crystal (LRPC) plate. Explicit matrix formulations are developed for the calculation of band structure. In order to illustrate the accuracy of the results, the band structure calculated by PWE method is compared to that calculated by finite element (FE) method. In addition, in order to reveal the bandgap properties, band structures of the “spring–mass” simplified model of stubbed-on LRPC plate, “spring–torsional spring–mass” simplified model of stubbed-on LRPC plate and “spring–torsional spring–mass” simplified model of composite LRPC plate with and without the viscidity considered are presented and investigated in detail.

Optimization and experimental validation of stiff porous phononic plates for widest complete bandgap of mixed fundamental guided wave modes

Abstract Phononic crystal plates (PhPs) have promising application in manipulation of guided waves for design of low-loss acoustic devices and built-in acoustic metamaterial lenses in plate structures. The prominent feature of phononic crystals is the existence of frequency bandgaps over which the waves are stopped, or are resonated and guided within appropriate defects. Therefore, maximized bandgaps of PhPs are desirable to enhance their phononic controllability. Porous PhPs produced through perforation of a uniform background plate, in which the porous interfaces act as strong reflectors of wave energy, are relatively easy to produce. However, the research in optimization of porous PhPs and experimental validation of achieved topologies has been very limited and particularly focused on bandgaps of flexural (asymmetric) wave modes. In this paper, porous PhPs are optimized through an efficient multiobjective genetic algorithm for widest complete bandgap of mixed fundamental guided wave modes (symmetric and asymmetric) and maximized stiffness. The Pareto front of optimization is analyzed and variation of bandgap efficiency with respect to stiffness is presented for various optimized topologies. Selected optimized topologies from the stiff and compliant regimes of Pareto front are manufactured by water-jetting an aluminum plate and their promising bandgap efficiency is experimentally observed. An optimized Pareto topology is also chosen and manufactured by laser cutting a Plexiglas (PMMA) plate, and its performance in self-collimation and focusing of guided waves is verified as compared to calculated dispersion properties.

Three-component pillared phononic crystal plate containing viscoelastic material

Three-component pillared phononic crystal plates (PPCPs) usually contain viscoelastic materials. The influence of viscoelasticity on the band structures cannot be ignored. Based on the finite element method (FEM) and the standard linear solid model, this paper proposes a method to obtain the band structures of three-component PPCP containing viscoelastic rubber. The influence of the rubber storage modulus shifting along with frequency on the vibration band gaps is investigated, and the band structures of loss factor under different relaxation time are obtained.

Tunability of band structures in a two-dimensional magnetostrictive phononic crystal plate with stress and magnetic loadings

Considering the magneto-mechanical coupling of magnetostrictive material, the tunability of in-plane wave propagation in two-dimensional Terfenol-D/epoxy phononic crystal (PC) plate is investigated theoretically by the plane wave expansion method. Two Schemes, i.e. magnetic field is rotated in x–y plane and x–z plane, are studied, respectively. The effects of amplitude and direction of magnetic field, pre-stress and geometric parameters are discussed. For Scheme-I, band gap reaches the maximum at an optimal angle 45° of magnetic field. However, the optimal angle is 0° for Scheme-II, because band gap decreases monotonically until disappears with the increasing angle. For both cases, higher-order band gaps generate and become stronger as magnetic field amplitude increases, while increasing compressive pre-stress has the opposite effect. Meanwhile, filling fraction plays a key role in controlling band gaps. These results provide possibility for intelligent regulation and optimal design of PC plates.