Wave Propagation In Phononic Crystals Research Articles

Topological design of hexagonal lattice phononic crystals for vibration attenuation combined fast plane wave expansion method with elite seed strategy genetic algorithm

The characteristics of manipulating elastic wave propagation in phononic crystals (PnCs) have been applied in various fields. A triangular element discrete method for two-dimensional (2D) hexagonal lattice PnCs is proposed, which combines with the fast plane wave expansion method (FPWEM) to obtain the band structure. As compared to the finite element method (FEM), time consumption is one order of magnitude faster while ensuring accuracy. To design the wider band gap (BG) of PnCs, the elite seed strategy genetic algorithm (ESS-GA) is used to optimize the topology of PnCs for in-plane mode and out-of-plane mode, and based on this, the proposed method is first applied to optimize hexagonal lattice PnCs, which is extended to the BG design of mixed mode. The relationship between the optimized individual under different propagate modes, and the volume fraction of PnCs at each BG is explained, physical mechanism of optimized unit cells is also estimated through iso-frequency contours and dynamic effective mass. The numerical and experimental results of a hexagonal lattice composed of optimized unit cells indicate that elastic waves can be suppressed within the BG, fully demonstrating the effectiveness of the method. In addition, this method is expected to explore its potential applications in the reverse design of PnCs.

Modeling of a lattice model for nonlinear wave propagation in phononic crystals

We construct a nonlinear lattice model to investigate the dynamics of nonlinear behavior in phononic crystals (PnCs). Two types of mass points and springs are introduced in the model to reproduce the difference in material properties between the scatterers and background in PnCs. The nonlinearity is introduced to the model by changing the mass of each mass point depending on the displacement gradient at the mass point. We numerically confirm that both the 1D and 2D models have the bandgap in the linear dispersion relation. Moreover, in both model, switching behavior of wave propagation is found.

Waves Propagating in Nano-Layered Phononic Crystals with Flexoelectricity, Microstructure, and Micro-Inertia Effects.

The miniaturization of electronic devices is an important trend in the development of modern microelectronics information technology. However, when the size of the component or the material is reduced to the micro/nano scale, some size-dependent effects have to be taken into account. In this paper, the wave propagation in nano phononic crystals is investigated, which may have a potential application in the development of acoustic wave devices in the nanoscale. Based on the electric Gibbs free energy variational principle for nanosized dielectrics, a theoretical framework describing the size-dependent phenomenon was built, and the governing equation as well as the dispersion relation derived; the flexoelectric effect, microstructure, and micro-inertia effects are taken into consideration. To uncover the influence of these three size-dependent effects on the width and midfrequency of the band gaps of the waves propagating in periodically layered structures, some related numerical examples were shown. Comparing the present results with the results obtained with the classical elastic theory, we find that the coupled effects of flexoelectricity, microstructure, and micro-inertia have a significant or even dominant influence on the waves propagating in phononic crystals in the nanoscale. With increase in the size of the phononic crystal, the size effects gradually disappear and the corresponding dispersion curves approach the dispersion curves obtained with the conventional elastic theory, which verify the results obtained in this paper. Thus, when we study the waves propagating in phononic crystals in the micro/nano scale, the flexoelectric, microstructure, and micro-inertia effects should be considered.

Deep learning of dispersion engineering in two-dimensional phononic crystals

To control wave propagation in phononic crystals (PnCs), it is crucial to perform the inverse design of dispersion engineering. In this article, a robust deep-learning method of dispersion engineering in two-dimensional (2D) PnCs is developed by combining deep neural networks (DNNs) with the genetic algorithm (GA), which can be easily extended to reach any target in the trained DNNs’ calculation domain. A high-precision and robust DNN model to predict the bounds of energy bands of 2D PnCs is proposed, forming the forward prediction process. This DNN model shows high efficiency in the testing structures while keeping the mean relative error near 0.1%. The inverse design of PnCs is implemented by DNNs combined with the GA, building the back–forward retrieval process, which can exactly produce the desired PnCs with the expected bandgap bounds in only a few seconds. The proposed framework is promising for constructing arbitrary PnCs on demand.

Thermal tuning of the interfacial adhesive layer on the band gaps in a one-dimensional phononic crystal

Phononic crystals possess unique acoustic properties due to their artificial periodic structure. They have been used in a wide range of applications such as wave guides, filters, noise suppression, vibration control, etc. In this paper, an analytic model based on the transfer matrix method is established to study the band gaps of P- and SH-waves in a one-dimensional phononic crystal consisting of alternating strips of two different materials bonded by an interfacial adhesive layer. The analysis accounting for the temperature dependent elastic property of the interfacial adhesive layer indicates a different but an effective approach for thermal tuning of the acoustic band structures. It is shown that the first band gap width may decrease over 50% as the temperature increases from 20°C to 80°C. These results provide design guidelines for thermal tuning of wave propagation in phononic crystals.

Modulated phononic crystals: Non-reciprocal wave propagation and Willis materials

Research on breaking time-reversal symmetry in wave phenomena is a growing area of interest in the field of phononic crystals and metamaterials aiming to realize one-way propagation devices which have many potential technological applications. Here we investigate wave propagation in phononic crystals, periodic laminates in particular, where both elastic moduli and mass density are modulated in space and time in a wave-like fashion. The modulation introduces a bias which breaks time-reversal symmetry and reciprocity. A full characterization of how the dispersion curve transforms due to wave-like modulations is given in analytical and geometrical terms for both low (subsonic) and high (supersonic) modulation speeds. Theoretical findings are supported by numerical simulations. More specific to low frequencies, the macroscopic constitutive law of 1, 2 and 3D modulated laminates is proven to be of the Willis type with a non-negligible Willis coupling in the strictly scale-separated homogenization limit. The existence of a macroscopic stress-velocity and momentum-strain Willis coupling is in fact directly related to the breaking of reciprocity. Finally, closed form expressions of the macroscopic constitutive parameters are obtained and some elementary yet insightful energy bounds are derived and discussed.

A mechanical-magneto-thermal model for the tunability of band gaps of epoxy/Terfenol-D phononic crystals

A way based on the temperature effect is investigated to adjust the longitudinal wave band gaps of one-dimensional epoxy/Terfenol-D phononic crystals. For both the cases (with and without consideration of demagnetization effect), the dependences of component materials' effective parameters on temperature are obtained by applying a nonlinear mechanical-magneto-thermal coupling constitutive model and fitting the experimental data, respectively. Further, the influence of temperature on the band structure of wave propagation in phononic crystals consisting of epoxy and Terfenol-D is discussed in detail. Meanwhile, the effects of magnetic field, pre-stress, and filling fraction are studied. Numerical results show that temperature has a significant influence on the band structure of wave propagation in phononic crystals: As temperature rises from −40 °C to 40 °C, the widths of the first, second, and fourth band gaps increase, while that of the third band gap decreases. In addition, the demagnetization effect should not be ignored under a low magnetic field.

Phononic crystals and elastodynamics: Some relevant points

In the present paper we review briefly some of the first works on wave propagation in phononic crystals emphasizing the conditions for the creation of acoustic band-gaps and the role of resonances to the band-gap creation. We show that useful conclusions in the analysis of phononic band gap structures can be drawn by considering the mathematical similarities of the basic classical wave equation (Helmholtz equation) with Schrödinger equation and by employing basic solid state physics concepts and conclusions regarding electronic waves. In the second part of the paper we demonstrate the potential of phononic systems to be used as elastic metamaterials. This is done by demonstrating negative refraction in phononic crystals and subwavelength waveguiding in a linear chain of elastic inclusions, and by proposing a novel structure with close to pentamode behavior. Finally the potential of phononic structures to be used in liquid sensor applications is discussed and demonstrated.

Laser-enabled experimental wavefield reconstruction in two-dimensional phononic crystals

Abstract During the past two decades, noteworthy experimental investigations have been conducted on wave propagation in phononic crystals, with special emphasis on crystals for acoustic wave control, consisting of the repetition of cylindrical or spherical elements in a fluid medium. On the other hand, the experimental characterization of the elastic wave phenomena observed in the solid microstructure of phononic crystals designed for elastic wave control has been quite sparse and limited in scope. The related literature focuses mostly on steady-state analyses that aim at highlighting filtering properties, and are limited to out-of-plane measurements. The scope of this work is to address these limitations and provide a detailed experimental characterization of the transient wave phenomena observed in the cores of lattice-like phononic crystals. This is achieved using a 3D Scanning Laser Vibrometer, which allows measuring the in-plane velocity of material points belonging to the lattice topology. This approach is tested against the benchmark case of a regular honeycomb lattice. Specifically, the objective is to demonstrate the directional and dispersive nature of the S-mode at relatively low frequencies and characterize the P-mode below and above its veering frequency. The experimental results are compared against numerical simulations and unit cell Bloch analysis to highlight similarities and differences between the true response of finite crystals and the infinite lattice approximation. This study also intends to highlight the advantages of three-dimensional laser vibrometry as a tool for the characterization of complex structural materials, while carefully exposing some limitations of this methodology.

Linear Defect States of Phononic Crystal Thin Plates – An Application of Finite Element Method

In this paper, propagation of flexural vibration in phononic crystal thin plates with straight, bending or branching linear defects are explored using finite element method. The plate is composed of an array of circular crystalline Al2O3 cylinders embedded periodically in the epoxy matrix with a square lattice. The numerical results showed that accurate band structures and transmission response curves could be obtained by finite element method compared with that of improved plane wave expansion method. The exploration indicated that finite element method is efficient and suitable in dealing with the wave propagation in phononic crystal, and displays potential abilities in dealing with complex structures.

Size-effect on band structures of nanoscale phononic crystals

The scaling law does not hold when the sizes of the phononic crystals reach the nanoscale dimension [Ramprasad et al., Applied Physics Letters 87 (2005) [9]]111101. This paper discusses the size-effect on the band structures of nanoscale phononic crystals. The transfer matrix method based on the nonlocal elastic continuum theory is developed to compute the band structures of a nanoscale layered phononic crystal. Detailed calculations are performed for a nanoscale HfO 2–ZrO 2 multilayer stack. It is shown that the nonlocal elastic continuum solution deviates from the classical elastic continuum one and finally approaches the first-principle result as the thickness of each individual layer decreases. When the thickness of each layer is much larger than several nanometers, the correspondence between the nonlocal and classical elastic methods is shown, and the size effects can be neglected. The developed nonlocal elastic continuum method is expected to overcome the limits of the classical continuum description for wave propagation in phononic crystals when dimensions are in nanometer-length scales.

1905 Band gap characteristics of elastic waves in phononic crystals with thermal stress

In this paper, the effects of the thermal stress on the elastic wave propagation in phononic crystals are investigated. Based on the Bloch theory and the plane wave expansion method, the expression of the generalized eigenvalue equation is derived. The band structures for the in-plane and out-of-plane modes are presented. The results show that the filling ratios corresponding to the maximums of the band gap for the in-plane mode and mode II of the out-of-plane mode are different. The band gap characteristics can be changed by the thermal stress. The larger the temperature variance is, the lower the band gap edges become.

Elastic waves in noncohesive frictionless granular crystals

An ordered structure of noncohesive spherical beads constitutes a phononic crystal. This type of media combines the properties of wave propagation in phononic crystals (dispersion due to the geometrical periodicity) with the properties of wave propagation in granular media (nonlinearities, rotational degree of freedom) and gives the opportunity to have interesting features as tunable frequency band gaps for example. In this work, the acoustic bulk modes of a hexagonal close packed (hcp) structure of beads, considered as rigid masses connected by springs, are theoretically evaluated and their associated resonance frequencies are compared to experimental results. When friction is neglected, the elastic interaction between the beads are reduced to a normal spring interaction given by the Hertz theory. According to this theory, the rigidity of the contact depends on its static loading. The theory predicts the existence of elastic transverse and longitudinal acoustical-type modes and transverse and longitudinal optical-type modes. The acoustic transfer function of a hcp crystal slab built with stainless steel beads is measured and its resonance frequencies are compared to the theoretical predictions. Despite some differences between theory and experiments, which could come for instance from the disordered character of the contact loads, the developed theory and the experimental results show relatively good agreement.

Review of phononic crystals, nonlinear processes, devices and prospects

The review of current state of the art of bulk and surface linear and nonlinear acoustic wave propagation in phononic crystals (PhC) is given. First, theoretical analysis of bulk acoustic waves propagation in 2D phononic crystals composed of elastic medium with periodic systems of air holes with different symmetry is considered. The properties of hypersonic bulk and surface acoustic waves (Love, Lamb) in PhC are considered theoretically and expermentally. We studied bulk waves propagation in microstructured optical fiber preforms made of quartz. The study of simultaneous propagation of acoustic waves and light in structures being both photonic and phononic crystals was done. We study also properties of guided waves (Lamb modes) propagating in layered structures containing the magnetic films with two‐dimensional periodic structures. In these structures we discovered a strong coupling between elastic and magnetic properties leading to effective waves transformation between magnetic and elastic systems. Such structures are so called magnonic‐phononic crystals. The recommendations of use such unusual BAW and SAW properties in PhC for development of solid state devices are given. This work is supported by RFBR grant 08‐02‐00785.

Acoustic wave propagation in one-dimensional phononic crystals containing Helmholtz resonators

One-dimensional acoustic waveguide containing subwavelength-sized Helmholtz resonators is known to exhibit novel physical phenomena. However, no systematic theoretical study on this system has been carried out so far except on a few limited cases. We present a thorough theoretical calculation on the acoustic wave propagation in phononic crystals containing Helmholtz resonators without any geometrical size restrictions. The band structures, transmission spectra, and defect states are studied for diverse geometries using the interface response theory. It is shown that the acoustic band structure of the model is fundamentally different from the conventional acoustic–elastic cases and richer due to the coexistence of the resonant and the Bragg gaps. It is also shown that the presence of a defect resonator in the system can give rise to a localized mode inside the resonance gaps. The results clearly show that the presence of the Helmholtz resonators singly or periodically can play a prominent role in designing any acoustic band gap materials.

Wave band gaps in two-dimensional piezoelectric/piezomagnetic phononic crystals

In this paper, the elastic wave propagation in phononic crystals with piezoelectric and piezomagnetic inclusions is investigated taking the magneto-electro-elastic coupling into account. The electric and magnetic fields are approximated as quasi-static. The band structures of three kinds of piezoelectric/piezomagnetic phononic crystals—CoFe 2O 4/quartz, BaTiO 3/CoFe 2O 4 and BaTiO 3–CoFe 2O 4/polymer periodic composites are calculated using the plane-wave expansion method. The piezoelectric and piezomagnetic effects on the band structures are analyzed. The numerical results show that in CoFe 2O 4/quartz structures, only one narrow band gap exists along the Γ– X direction for the coupling of xy-mode and z-mode for the filling fraction f being 0.4; while in BaTiO 3/CoFe 2O 4 composites, only one narrow band gap exists along the Γ– X direction for xy-mode and no band gap exists for z-mode as the filling friction f is 0.5. Moreover, for the new type of magneto-electro-elastic phononic crystal—BaTiO 3–CoFe 2O 4/polymer periodic composite, the band gap characteristics are more superior in the whole considered frequency regions due to the big contrast of the material properties in the two constituents and the effects of the piezoelectricity and piezomagneticity on the band gap structures are remarkable.

Theoretical study of two-dimensional phononic crystals with viscoelasticity based on fractional derivative models

Wave propagation in two-dimensional phononic crystals (PCs) with viscoelasticity is investigated using a finite-difference-time-domain (FDTD) method. The viscoelasticity is evaluated using the Kelvin–Voigt model with fractional derivatives (FDs) so that both the dispersion and dissipation are considered. Numerical approximation of FDs is integrated into the FDTD scheme to simulate wave propagation in such PCs. All the constituent materials are treated as isotropic and homogeneous. The gaps are substantially displaced and widened and the attenuation is noticeably enhanced due to the dispersion and dissipation of host material and the complicated multiple scattering between scatterers. These results indicate that the viscoelasticity of the damping host has significant influence on wave propagation in PCs and should be considered.

Explicit dynamic finite element method for band-structure calculations of 2D phononic crystals

A fluid–solid coupling numerical algorithm based on explicit dynamic finite element method (DFEM) for band-structure calculation in phononic crystals is presented. Numerical examples are developed for 2D square phononic lattice with Au cylinders in epoxy matrix, and mercury cylinders in Al matrix. The results are compared with those calculated by FDTD and PWE methods, which indicate that DFEM is efficient in dealing with the wave propagation in phononic crystals, and displays potential abilities in dealing with anisotropic and nonlinear problems.

The directional propagation characteristics of elastic wave in two-dimensional thin plate phononic crystals

Abstract The directional propagation characteristics of elastic wave during pass bands in two-dimensional thin plate phononic crystals are analyzed by using the lumped-mass method to yield the phase constant surface. The directions and regions of wave propagation in phononic crystals for certain frequencies during pass bands are predicted with the iso-frequency contour lines of the phase constant surface, which are then validated with the harmonic responses of a finite two-dimensional thin plate phononic crystals with 16 × 16 unit cells. These results are useful for controlling the wave propagation in the pass bands of phononic crystals.