Dimensional Phononic Crystal Research Articles

Band gaps of elastic waves in 1-D dielectric phononic crystal with the flexoelectric and strain gradient effects consideration

The propagation of Bloch waves in one dimensional phononic crystal consisting of dielectric elastic solids is studied with consideration of the strain gradient, inertial gradient and flexoelectric effects. The transfer matrixes for single layer and one-cell of phononic structure are derived based on the constitutive equations and the governing equations of dielectric elastic solids. The dispersion equation for Bloch waves is obtained by the application of periodic conditions for the generalized displacements and tractions considered within strain gradient theory of electro-elasticity. Based on the numerical solution of the derived dispersion equation, the influences of the micro-stiffness length scale, micro-inertial length scale and flexoelectric coefficients on the dispersion and the bandgap are discussed.

Enhanced anchor quality factor of an aluminium nitride-on-silicon MEMS resonator using support tethers based on compound leaf-shaped one dimensional phononic crystal

Enhanced anchor quality factor of an aluminium nitride-on-silicon MEMS resonator using support tethers based on compound leaf-shaped one dimensional phononic crystal

Mechanical vibration absorber for flexural wave attenuation in multi-materials metastructure

Vibration isolation is a promise to suppress mechanical vibration from a host structure, similarly, a mechanical vibration absorber, a simple but effective device to attenuate flexural wave propagation, which has been implemented in civil and mechanical engineering. This paper presents a type of composite sandwich phononic crystal to attenuate the flexural wave propagation in a beam structure, which can effectively suppress mechanical vibration in a broad band gap by repetitively arranging phononic crystal. First, the elastic wave dispersion characteristic in a composite sandwich beam structure is derived, and a triangular shape phononic crystal for flexural wave attenuation by taking advantage of destructive interference is presented. Then two dimensional phononic crystals are designed by assembling four different unit-cells of metabeam. Finally, numerical experiments are conducted to verify the effectiveness of the proposed mechanical metamaterial absorbers to attenuate flexural wave propagation, the numerical results indicate that the proposed metamaterial is of good performance in mechanical vibration suppression, which can effectively mitigate structure vibration in low-frequency domain than the structure without phononic crystal and single layer metamaterial beam structure. It is the first attempt to design a mechanical metamaterial absorber with the mechanism of destructive interference with composite sandwich phononic crystal.

The Influence of Medium Movement on the Occurrence of Band Gaps in Quasi Two Dimensional Phononic Crystals

The Influence of Medium Movement on the Occurrence of Band Gaps in Quasi Two Dimensional Phononic Crystals

Design of a Thickness Sensor Based on a One-Dimensional Phononic Crystal

Nowadays, sensor technology has attracted great interest in various domains. In this ‎work, we have analyzed a one dimensional phononic crystal made by the stack of N bilayers of ‎‎(LiNbO3/SiO2). The sensor design consists of a one dimensional phononic crystal structure with a ‎defect layer inserted in the middle. Using the Transfer Matrix Method (TMM), the transmission ‎spectrums of acoustic waves are calculated and plotted. In this work, we are interested in the ‎resonance peak that is transmitted inside the phononic band gap. The results obtained show clearly that the resonant frequency of the measured ‎transmission peak is very sensitive to the layer defect properties. This proves that such structure offers a new platform for sensing ‎applications.

Tunable topological edge states and rainbow trapping in two dimensional magnetoelastic phononic crystal plates based on an external magnetostatic field

The elastic analogs of topological insulators (TIs) have attracted substantial research interest owing to their potential prospects in wave manipulation and low-loss transmission. However, most work in solid phononic crystal (PC) systems suffering from fixed-structure restrictions lack the active tunability of topological edge states, hindering their practical applications in dynamic situations. Here, we present a new design of tunable elastic TIs made up of smart magnetostrictive materials and perforated silicon plates. The topological phase transition is induced by altering the spatial intensity distribution of external magnetostatic field. Placing two topologically distinct magnetoelastic PC plates adjacent to each other, the pseudospin-Hall edge modes for plate-mode waves are obtained at the interface between them. Moreover, the reconfigurable propagation route and topological robustness of edge states are demonstrated by numerical simulations. Finally, the frequency and group velocity of edge modes can be continuously adjusted by an interfacial magnetic field. Utilizing such a contactless tunability, a reconfigurable topological rainbow is attained by reconstructing the gradient-descent interfacial magnetic field along the topological interface. The proposed system with magnetically tunable edge states can become a stepping-stone platform towards the designs of elastic wave devices with more applicability for dynamic conditions, such as waveguides, energy harvesters and buffers.

Study on Band Gap Characteristics of Boat-Shaped Phononic Crystal

In this paper, we analyze the two-dimensional Boat-shaped structure based on the finite element method. We calculated its energy band structure and vibration transmission properties and found that the structure has band gaps at both high and low frequencies. Compared with common traditional two- dimensional phononic crystals, the boat-shaped phononic crystal has the advantage of larger bandgap design and modulation parameter space due to their structural complexity. In order to obtain better bandgap characteristics, we studied the influence of four key parameters, such as the rod length and the angle between the rods, on the bandgap. The results show that: for low frequency band gaps, the width of the band gap can be effectively changed by changing the size of the angle between the rods while rod length greatly affects the bandgap position; for high band gaps, the length of rods has a large effect on the band gap position. These laws have guiding significance for the bandgap regulation of boat-shaped phononic crystal.

Dispersion relations of anti-plane elastic waves in micro-scale one dimensional piezoelectric semiconductor phononic crystals with the consideration of interface effect

In this paper, the propagation properties of anti-plane elastic waves in a piezoelectric semiconductor (PS) layered periodic composites are theoretically investigated. The periodic layered composites consist of periodically repeated two micro-scale geometrical thickness PS slabs with different elasticity, piezoelectricity and charge carriers. Following consideration of the coupling mechanical anti-plane displacement, electric potential and perturbation of charge carriers, the influences of interface effects resulted from homo- and hetero-junctions on the dispersion relations of anti-plane elastic waves are systematically discussed. It is found that homo- and hetero-junctions can be approximately treated as rigid imperfect interfaces, which can enhance the width of band-gaps of anti-plane elastic waves, especially for high-frequency short-wavelength anti-plane elastic waves. The establishment of mathematical models and the revelation of physical mechanisms are all fundamental to the analysis and optimization of micro-scale energy harvesters based on the propagation of anti-plane elastic waves.

Acoustic Zitterbewgung of the shear stress field in two-dimensional phononic crystals with electroreological material

Theoretically the paper confirmed the existence of the acoustic Zitterbewegung of the shear stress field in two dimensional phononic crystals, in which epoxy insects arranged in square are embedded in an electroreological material matrix. The shear storage modulus, the loss modulus of electroreological material, and the band gaps of the phononic crystals are changed with electric field strength. Therefore, the oscillatory period and amplitude of the acoustic Zitterbewegung of the shear stress field can be controlled by external voltages. This could be of importance in designing an experiment to investigate the acoustic Zitterbewegung of the shear stress field in two dimensional phononic crystals with electroreological material matrix.

Locally resonant phononic crystals band-gap analysis on a two dimensional phononic crystal with a square and a triangular lattice

Locally resonant phononic crystals (LRPC) are a new type of sound insulating material. Using the plane wave expansion method based on the Bloch theorem, we compute the band structure of two dimensional (2D) phononic crystals (PC) with square and triangular lattices. Such PC typically consists of infinitely long carbon rods coated with silicon rubber and embedded in an elastic background. Computational results show that gaps appear at the lower frequency range, which are lower than those expected from the Bragg mechanism. Those gaps are generated due to local resonances; the optimum gap is obtained by tuning the thickness ratio of the coating layer. The gap created by the LRPC depends on the filling fraction of the coating cylinders.

Zone folding induced tunable topological interface states in one-dimensional phononic crystal plates

In previous literature, the realization of topological interface state in one-dimensional periodic system is strongly relied on the tedious parameter adjustment to search for the Dirac cone. In this paper, based on a strategy of zone folding, multiple topological interface modes for the shear horizontal guided waves in one dimensional phononic crystal plate are investigated by using finite element method and eigenmode matching theory, in which the Dirac points are formed by simply making the unit cell double. Significantly, by simply contracting or expanding the stubs can bring the topological phase transition. Furthermore, the topological phase transition is further achieved by varying the height of the stubs. The proposed designs will be more convenient to be applied in real engineering.

Concentric Split Aluminum with Silicon-Aluminum Nitride Annular Rings Resonators.

This paper presents a novel approach of annular concentric split rings microelectromechanical resonators with tether configuration to reduce anchor loss and gives very high-quality factor (Q) 2.97 Million based on FEA (Finite Element Analysis) simulation. The operating frequencies of these resonators are 188.55 MHz to 188.62 MHz. When the proposed SR (square rectangle) hole shaped one dimensional phononic crystal (1D PnC), and two dimensional phononic crystal (2D PnC) structure consist of very wide and complete band gaps is applied to novel design rings MEMS resonators, the quality factor (Q) further improved to 19.7 Million and 1750 Million, respectively, by using the finite element method. It is also observed that band gaps become closer by reducing the value of filling fraction, and proposed SR PnC gives extensive peak attenuation. Moreover, harmonic response of ring resonator is verified by the perfect match layers (PML) technique surrounded by resonators with varying width 1.5λ, and 3λ effectively reduce the vibration displacement.

Tunability of hysteresis-dependent band gaps in a two-dimensional magneto-elastic phononic crystal using magnetic and stress loadings

A quasistatic hysteresis model is established to investigate the performance of elastic wave propagation in two dimensional magneto-elastic phononic crystals (PCs) with the nonlinear magneto-mechanical coupling hysteretic constitutive behavior of magnetostrictive materials when subjected to magnetic field and pre-stress. Through the example of Terfenol-D/epoxy PCs, it is revealed that the characteristics of band structures are hysteresis-dependent and remarkably affected by pre-stress due to the nature of the hysteresis behavior for Terfenol-D. Consequently, the study of hysteresis induced band structures in magneto-elastic PCs is significant and essential for intelligent regulation of phononic devices in engineering.

Inherent negative refraction on acoustic branch of two dimensional phononic crystals

Guided by theoretical predictions, we have demonstrated experimentally the existence of negative refraction on the two lowest acoustic-branch passbands (shear and longitudinal modes) of a simple two-dimensional phononic crystal consisting of an isotropic stiff (aluminum) matrix and square-patterned isotropic compliant (PMMA) circular inclusions. We experimentally distinguished the shear and longitudinal modes to ensure that there are no couplings between the two modes and that the shear-mode negative refraction is an inherent property of periodic composites with stiff matrix and compliant inclusions. We have also discovered that a composite with compliant (PMMA) matrix and stiff (aluminum) inclusions does not display negative shear-mode refraction on its first branch. At frequencies and wave vectors where the refraction on the acoustic-branch passbands is negative, the effective mass-density and the effective stiffness tensors of the crystal are positive-definite, and this is an inherent property of such phononic crystals.The equi-frequency contours and energy flux vectors as functions of the phase-vector components, reveal a rich body of refractive properties that can be exploited to realize, for example, beam splitting, focusing, and frequency filtration on the lowest passbands of the crystal where the dissipation is minimum. By proper selection of material and geometric parameters these phenomena can be realized at remarkably low frequencies (large wave lengths) using rather small simple two-phase unit cells.

Seismic isolation of buildings on two dimensional phononic crystal foundation

In order to realize the seismic isolation of buildings, we establish the two dimensional phononic crystal (PC) foundation which has the cell with the size close to the regular concrete test specimens, and is composed of the concrete base, rubber coating and lead cylindrical core. We study the in-plane band gap (BG) characteristics in it, through the analysis of the frequency dispersion relation and frequency response result. To lower the start BG frequency to the seismic frequency range, we also study the influences of material parameters (the elastic modulus of coating and density of cylindrical core) and geometry parameters (the thickness of coating, radius of cylindrical core and lattice constant) on BG ranges. The study could help to design the PC foundation for seismic isolation of building.

Higher order interfacial effects for elastic waves in one dimensional phononic crystals via the Lagrange-Hamilton's principle

Abstract This work proposes new transmission conditions at the interfaces between the layers of a three-dimensional composite structures. The proposed transmission conditions are obtained by applying the asymptotic expansion technique in the framework of Lagrange-Hamilton's principle. The proposed conditions take into account interfacial effects of higher order, thus representing an extension of the classical zero-thickness interface models. In particular, the (small) thickness of the interface together with its inertia, stiffness and anisotropy are accounted for. The effect of the transmission conditions on the band structure of Bloch–Floquet waves propagating in a one dimensional phononic crystal is discussed based on numerical results.

The Schoch effect mechanism analysis and its regulation of two dimensional three components phononic crystal

In this paper, through changing the phononic crystal surface and adjusting the structure of surface layer, we observed the Schoch effect of two dimensional phononic crystal, and the Schoch shift reached 7.1 times of the lattice constant. To further understand the physical mechanism of this kind of phenomenon, the finite element method is used to calculate the band structure of the model. Because of the influences of the surface of structure, there exists a kind of waveguide mode in the passband. Through careful analysis of the band structure and the sound pressure field profile, it is found the kind of waveguide mode makes the incident wave energy go into the waveguide layer which resulting in reflection beam deformation and offset. In addition, through the finite element simulation, the change regulation of the Schoch shift in the phononic crystal is studied by changing the radius of the surface layer and further increase the layer number of the surface layer of the phononic crystal to achieve the control of the Schoch effect of the phononic crystal. The conclusion of this paper can provide some theoretical reference and give some guidance for the design of acoustic sensors based on Schoch effect.

GHz spurious mode free AlN lamb wave resonator with high figure of merit using one dimensional phononic crystal tethers

This letter reports a spurious mode free GHz aluminum nitride (AlN) lamb wave resonator (LWR) towards high figure of merit (FOM). One dimensional gourd-shape phononic crystal (PnC) tether with large phononic bandgaps is employed to reduce the acoustic energy dissipation into the substrate. The periodic PnC tethers are based on a 1 μm-thick AlN layer with 0.26 μm-thick Mo layer on top. A clean spectrum over a wide frequency range is obtained from the measurement, which indicates a wide-band suppression of spurious modes. Experimental results demonstrate that the fabricated AlN LWR has an insertion loss of 5.2 dB and a loaded quality factor (Q) of 1893 at 1.02 GHz measured in air. An impressive ratio of the resistance at parallel resonance (Rp) to the resistance at series resonance (Rs) of 49.8 dB is obtained, which is an indication of high FOM for LWR. The high Rp to Rs ratio is one of the most important parameters to design a radio frequency filter with steep roll-off.

Thermoelectric properties of nanoscale three dimensional Si phononic crystals

The thermoelectric properties of n-type nanoscale three dimensional (3D) Si phononic crystals (PnCs) with spherical pores are studied. Density functional theory and Boltzmann transport equation under the relaxation time approximation are applied to study the electronic transport coefficients, electrical conductivity, Seebeck coefficient and electronic thermal conductivity. We found that the electronic transport coefficients in 3D Si PnC at room temperature (300K) is reduced slightly compared with that of bulk Si, for example, electrical conductivity and electronic thermal conductivity is decreased by 22–39% and 30–43% depending on carrier concentration, respectively, and the Seebeck coefficient is similar to that of bulk Si. However, the lattice thermal conductivity of 3D Si PnCs with spherical pores is decreased 500 times calculated by molecular dynamics methods, leading to the ZT=0.66 at carrier concentration around 2.66×1019cm−3, which is about 26 times of that of porous Si. This work suggests that 3D Si PnC is a promising candidate for high efficiency thermoelectric materials.

Coherent heat transport in 2D phononic crystals with acoustic impedance mismatch

In this work we have calculated the cumulative thermal conductivities of micro-phononic crystals formed by different combinations of inclusions and matrices at a sub-Kelvin temperature regime. The low-frequency phonon spectra (up to tens of GHz) were obtained by solving the generalized wave equation for inhomogeneous media with the plane wave expansion method. The thermal conductivity was calculated from Boltzmann transport theory highlighting the role of the low-frequency thermal phonons and neglecting phonon–phonon scattering. A purely coherent thermal transport regime was assumed throughout the structures. Our findings show that the cumulative thermal conductivity drops dramatically when compared with their bulk counterpart. Depending on the structural composition this reduction may be attributed to the phonon group velocity due to a flattening of the phonon dispersion relation, the extinction of phonon modes in the density of states or due to the presence of complete band gaps. According to the contrast between the inclusions and the matrices, three types of two dimensional phononic crystals were considered: carbon/epoxy, carbon/polyethylene and tungsten/silicon, which correspond respectively to a moderate, strong and very strong mismatch in the mechanical properties of these materials.