Special Issue "Phononic Crystals"

A special issue of Crystals (ISSN 2073-4352). This special issue belongs to the section "Crystal Engineering".

Deadline for manuscript submissions: closed (31 March 2016)

Special Issue Editors

Guest Editor
Prof. Dr. Victor J. Sanchez-Morcillo

Department of Applied Physics, Universitat Politècnica de València, , 46730 Gandia, Spain
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Interests: nonlinear dynamics; ultrasound; phononic crystals
Guest Editor
Dr. Vicent Romero-Garcia

Researcher at CNRS Laboratoire d'Acoustique de l'Université du Maine, UMR-CNRS 6613
Website | E-Mail
Interests: acoustic metamaterials; acoustic metasurfaces; perfect absorption; phononic crystals
Guest Editor
Dr. Luis M. Garcia-Raffi

Department of Applied Mathematics, Universitat Politècnica de València, 46022 València Spain
Website | E-Mail
Interests: sonic crystals; quasyperiodic; fractal and disordered structures; superlattices

Special Issue Information

Dear Colleagues,

Phononic crystals are periodic structures for phonons or acoustic/elastic waves, in close analogy to the crystalline structures for electrons. Due to the artificial periodicity and the associated temporal and spatial dispersion, they offer many possibilities to control the propagation of waves. Phenomena not found in conventional matter, as the formation of band gaps, negative refraction, beam self-collimation, subwavelength imaging, localization, waveguiding, and many others, have been exhaustively studied during the last years. Many of these phenomena are related to Bragg scattering effects that become relevant at wavelengths comparable with the periodicity of the system.

The field of phononics is progressing very quickly, being a main part of the current acoustics and vibration research worldwide, and extends beyond the simple periodic structures proposed initially. An extension of the main concepts to other materials, presenting remnants of order, as quasicrystals or random structures, or an increase of complexity by adding elements with a local response, as resonators and membranes, have been shown also relevant to the control of waves in structured media. Finally, nonlinear effects, as those shown by granular crystals, also add new degrees of freedom and open new perspectives in the field of acoustic/elastic wave control.

The current Special Issue of Crystals provides a unique forum for discussion and presentation of recent advances in the fields of research related to phononic crystals. Scientists working in this broad field, including quasicrystals or quasiperiodic structures for acoustic/elastic waves, are invited to present their work in this issue.

The topics summarized under the keywords should be considered only as examples. The volume is open for any advanced topics in the field of Phononic Crystals.

Prof. Dr. Victor J. Sanchez-Morcillo
Dr. Vicent Romero-Garcia
Dr. Luis M. Garcia-Raffi
Guest Editors

Manuscript Submission Information

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Keywords

  • phononic crystals
  • sonic crystals
  • granular crystals
  • waveguides
  • localization
  • focusing
  • band gaps

Published Papers (11 papers)

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Research

Open AccessArticle Coupled Acoustic-Mechanical Bandgaps
Crystals 2016, 6(9), 112; doi:10.3390/cryst6090112
Received: 30 April 2016 / Revised: 9 August 2016 / Accepted: 5 September 2016 / Published: 8 September 2016
Cited by 1 | PDF Full-text (2351 KB) | HTML Full-text | XML Full-text
Abstract
In this work, we study the existence of coupled bandgaps for corrugated plate structures and acoustic channels. The study is motivated by the observation that the performance of traditional bandgap structures, such as periodic plates, may be compromised due to the coupling to
[...] Read more.
In this work, we study the existence of coupled bandgaps for corrugated plate structures and acoustic channels. The study is motivated by the observation that the performance of traditional bandgap structures, such as periodic plates, may be compromised due to the coupling to a surrounding acoustic medium and the presence of acoustic resonances. It is demonstrated that corrugation of the plate structure can introduce bending wave bandgaps and bandgaps in the acoustic domain in overlapping and audible frequency ranges. This effect is preserved also when taking the physical coupling between the two domains into account. Additionally, the coupling is shown to introduce extra gaps in the band structure due to modal interaction and the appearance of a cut-on frequency for the fundamental acoustic mode. Full article
(This article belongs to the Special Issue Phononic Crystals)
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Open AccessArticle Second-Harmonic Generation in Membrane-Type Nonlinear Acoustic Metamaterials
Crystals 2016, 6(8), 86; doi:10.3390/cryst6080086
Received: 11 April 2016 / Revised: 21 July 2016 / Accepted: 25 July 2016 / Published: 29 July 2016
Cited by 2 | PDF Full-text (522 KB) | HTML Full-text | XML Full-text
Abstract
We study analytically and numerically the second-harmonic generation in a one-dimensional nonlinear acoustic metamaterial, composed of an air-filled waveguide periodically loaded by clamped elastic plates. Based on the transmission line approach, we derive a nonlinear dynamical lattice model which, in the continuum approximation,
[...] Read more.
We study analytically and numerically the second-harmonic generation in a one-dimensional nonlinear acoustic metamaterial, composed of an air-filled waveguide periodically loaded by clamped elastic plates. Based on the transmission line approach, we derive a nonlinear dynamical lattice model which, in the continuum approximation, leads to a nonlinear dispersive wave equation. By applying the perturbation method to the latter, we derive the analytical expressions for the first- and second-harmonics, which are in excellent agreement with the numerical simulations of the nonlinear dynamical lattice model. Apart from the case of dispersionless nonlinear propagation and the Fubini solution, special attention is payed to the role of dispersion. In that regard, it is found that, once dispersion comes into play, second-harmonic beatings in space due to phase-mismatch can be identified. Our results provide many opportunities for the development of new periodic acoustic structures featuring both nonlinearity and dispersion. Full article
(This article belongs to the Special Issue Phononic Crystals)
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Open AccessFeature PaperArticle Soda Cans Metamaterial: A Subwavelength-Scaled Phononic Crystal
Crystals 2016, 6(7), 82; doi:10.3390/cryst6070082
Received: 20 May 2016 / Revised: 6 July 2016 / Accepted: 19 July 2016 / Published: 21 July 2016
Cited by 3 | PDF Full-text (13575 KB) | HTML Full-text | XML Full-text
Abstract
Photonic or phononic crystals and metamaterials, due to their very different typical spatial scales—wavelength and deep subwavelength—and underlying physical mechanisms—Bragg interferences or local resonances—, are often considered to be very different composite media. As such, while the former are commonly used to manipulate
[...] Read more.
Photonic or phononic crystals and metamaterials, due to their very different typical spatial scales—wavelength and deep subwavelength—and underlying physical mechanisms—Bragg interferences or local resonances—, are often considered to be very different composite media. As such, while the former are commonly used to manipulate and control waves at the scale of the unit cell, i.e., wavelength, the latter are usually considered for their effective properties. Yet we have shown in the last few years that under some approximations, metamaterials can be used as photonic or phononic crystals, with the great advantage that they are much more compact. In this review, we will concentrate on metamaterials made out of soda cans, that is, Helmholtz resonators of deep subwavelength dimensions. We will first show that their properties can be understood, likewise phononic crystals, as resulting from interferences only, through multiple scattering effects and Fano interferences. Then, we will demonstrate that below the resonance frequency of its unit cell, a soda can metamaterial supports a band of subwavelength varying modes, which can be excited coherently using time reversal, in order to beat the diffraction limit from the far field. Above this frequency, the metamaterial supports a band gap, which we will use to demonstrate cavities and waveguides, very similar to those obtained in phononic crystals, albeit of deep subwavelength dimensions. We will finally show that multiple scattering can be taken advantage of in these metamaterials, by correctly structuring them. This allows to turn a metamaterial with a single negative effective property into a negative index metamaterial, which refracts waves negatively, hence acting as a superlens. Full article
(This article belongs to the Special Issue Phononic Crystals)
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Open AccessArticle Magnetic-Sphere-Based Phononic Crystals
Crystals 2016, 6(7), 78; doi:10.3390/cryst6070078
Received: 24 May 2016 / Revised: 28 June 2016 / Accepted: 1 July 2016 / Published: 8 July 2016
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Abstract
Periodic arrays in one, two, and three dimensions, made of magnetic spheres embedded in a fluid matrix, are considered in this study and utilized as phononic structures. The propagation of acoustic waves through these structures is analyzed experimentally, in low- and high-frequency region,
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Periodic arrays in one, two, and three dimensions, made of magnetic spheres embedded in a fluid matrix, are considered in this study and utilized as phononic structures. The propagation of acoustic waves through these structures is analyzed experimentally, in low- and high-frequency region, via laser vibrometry, as well as standard underwater acoustic measurements. A first comparison to theoretical calculations obtained through multiple-scattering techniques and multipole models reveals a distinct behavior depending on the immersion fluid and/or frequency regime. Our results show that the elastodynamic response of these systems can be, under conditions, simply described by classical elastic theory without taking directly (ab initio) into account the magnetic character of the spherical particles. The structures considered above could offer several possibilities including facility of construction and use in filtering applications, but they are also of interest from a theoretical point of view, as a means to investigate the validity of several approximate theoretical descriptions. Full article
(This article belongs to the Special Issue Phononic Crystals)
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Open AccessArticle Low-Temperature Coherent Thermal Conduction in Thin Phononic Crystal Membranes
Crystals 2016, 6(6), 72; doi:10.3390/cryst6060072
Received: 21 April 2016 / Revised: 13 June 2016 / Accepted: 16 June 2016 / Published: 22 June 2016
Cited by 6 | PDF Full-text (512 KB) | HTML Full-text | XML Full-text
Abstract
In recent years, the idea of controlling phonon thermal transport coherently using phononic crystals has been introduced. Here, we extend our previous numerical studies of ballistic low-temperature heat transport in two-dimensional hole-array phononic crystals, and concentrate on the effect of the lattice periodicity.
[...] Read more.
In recent years, the idea of controlling phonon thermal transport coherently using phononic crystals has been introduced. Here, we extend our previous numerical studies of ballistic low-temperature heat transport in two-dimensional hole-array phononic crystals, and concentrate on the effect of the lattice periodicity. We find that thermal conductance can be either enhanced or reduced by large factors, depending on the the lattice period. Analysis shows that both the density of states and the average group velocity are strongly affected by the periodic structuring. The largest effect for the reduction seen for larger period structures comes from the strong reduction of the group velocities, but a contribution also comes from the reduction of the density of states. For the short period structures, the enhancement is due to the enhanced density of states. Full article
(This article belongs to the Special Issue Phononic Crystals)
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Open AccessArticle Phononic Crystal Plate with Hollow Pillars Actively Controlled by Fluid Filling
Crystals 2016, 6(6), 64; doi:10.3390/cryst6060064
Received: 6 April 2016 / Revised: 14 May 2016 / Accepted: 19 May 2016 / Published: 24 May 2016
Cited by 8 | PDF Full-text (4944 KB) | HTML Full-text | XML Full-text
Abstract
We investigate theoretically the properties of phononic crystal plates with hollow pillars. Such crystals can exhibit confined whispering gallery modes around the hollow parts of the pillars whose localization can be increased by separating the pillar from the plate by a full cylinder.
[...] Read more.
We investigate theoretically the properties of phononic crystal plates with hollow pillars. Such crystals can exhibit confined whispering gallery modes around the hollow parts of the pillars whose localization can be increased by separating the pillar from the plate by a full cylinder. We discuss the behaviors of these modes and their potential applications in guiding and filtering. Filling the hollow parts with a fluid gives rise to new localized modes, which depend on the physical properties and height of the fluid. Thus, these modes can be actively controlled for the purpose of multichannel multiplexing. In particular, one can obtain localized modes associated with the compressional vibrations of the fluid along its height. They can be used for the purpose of sensing the acoustic properties of the fluid or their variations with temperature. Full article
(This article belongs to the Special Issue Phononic Crystals)
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Open AccessArticle Broadband Transmission Loss Using the Overlap of Resonances in 3D Sonic Crystals
Crystals 2016, 6(5), 51; doi:10.3390/cryst6050051
Received: 25 March 2016 / Revised: 25 April 2016 / Accepted: 3 May 2016 / Published: 11 May 2016
PDF Full-text (824 KB) | HTML Full-text | XML Full-text
Abstract
The acoustic properties of a three-dimensional sonic crystal made of square-rod rigid scatterers incorporating a periodic arrangement of quarter wavelength resonators are theoretically and experimentally reported in this work. The periodicity of the system produces Bragg band gaps that can be tuned in
[...] Read more.
The acoustic properties of a three-dimensional sonic crystal made of square-rod rigid scatterers incorporating a periodic arrangement of quarter wavelength resonators are theoretically and experimentally reported in this work. The periodicity of the system produces Bragg band gaps that can be tuned in frequency by modifying the orientation of the square-rod scatterers with respect to the incident wave. In addition, the quarter wavelength resonators introduce resonant band gaps that can be tuned by coupling the neighbor resonators. Bragg and resonant band gaps can overlap allowing the wave propagation control inside the periodic resonant medium. In particular, we show theoretically and experimentally that this system can produce a broad frequency band gap exceeding two and a half octaves (from 590 Hz to 3220 Hz) with transmission lower than 3%. Finite element methods were used to calculate the dispersion relation of the locally resonant system. The visco-thermal losses were accounted for in the quarter wavelength resonators to simulate the wave propagation in the semi-infinite structures and to compare the numerical results with the experiments performed in an echo-free chamber. The simulations and the experimental results are in good agreement. This work motivates interesting applications of this system as acoustic audible filters. Full article
(This article belongs to the Special Issue Phononic Crystals)
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Open AccessArticle Formation of Bragg Band Gaps in Anisotropic Phononic Crystals Analyzed With the Empty Lattice Model
Crystals 2016, 6(5), 52; doi:10.3390/cryst6050052
Received: 25 March 2016 / Revised: 25 April 2016 / Accepted: 3 May 2016 / Published: 11 May 2016
Cited by 1 | PDF Full-text (3801 KB) | HTML Full-text | XML Full-text
Abstract
Bragg band gaps of phononic crystals generally, but not always, open at Brillouin zone boundaries. The commonly accepted explanation stems from the empty lattice model: assuming a small material contrast between the constituents of the unit cell, avoided crossings in the phononic band
[...] Read more.
Bragg band gaps of phononic crystals generally, but not always, open at Brillouin zone boundaries. The commonly accepted explanation stems from the empty lattice model: assuming a small material contrast between the constituents of the unit cell, avoided crossings in the phononic band structure appear at frequencies and wavenumbers corresponding to band intersections; for scalar waves the lowest intersections coincide with boundaries of the first Brillouin zone. However, if a phononic crystal contains elastically anisotropic materials, its overall symmetry is not dictated solely by the lattice symmetry. We construct an empty lattice model for phononic crystals made of isotropic and anisotropic materials, based on their slowness curves. We find that, in the anisotropic case, avoided crossings generally do not appear at the boundaries of traditionally defined Brillouin zones. Furthermore, the Bragg “planes” which give rise to phononic band gaps, are generally not flat planes but curved surfaces. The same is found to be the case for avoided crossings between shear (transverse) and longitudinal bands in the isotropic case. Full article
(This article belongs to the Special Issue Phononic Crystals)
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Open AccessArticle Analysis of Longitudinal Waves in Rod-Type Piezoelectric Phononic Crystals
Crystals 2016, 6(4), 45; doi:10.3390/cryst6040045
Received: 14 February 2016 / Revised: 28 March 2016 / Accepted: 12 April 2016 / Published: 18 April 2016
Cited by 1 | PDF Full-text (7649 KB) | HTML Full-text | XML Full-text
Abstract
Phononic crystals can be used to control elastic waves due to their frequency bands. This paper analyzes the passive and active control as well as the dispersion properties of longitudinal waves in rod-type piezoelectric phononic crystals over large frequency ranges. Based on the
[...] Read more.
Phononic crystals can be used to control elastic waves due to their frequency bands. This paper analyzes the passive and active control as well as the dispersion properties of longitudinal waves in rod-type piezoelectric phononic crystals over large frequency ranges. Based on the Love rod theory for modeling the longitudinal wave motions in the constituent rods and the method of reverberation-ray matrix (MRRM) for deriving the member transfer matrices of the constituent rods, a modified transfer matrix method (MTMM) is proposed for the analysis of dispersion curves by combining with the Floquet–Bloch principle and for the calculation of transmission spectra. Numerical examples are provided to validate the proposed MTMM for analyzing the band structures in both low and high frequency ranges. The passive control of longitudinal-wave band structures is studied by discussing the influences of the electrode’s thickness, the Poisson’s effect and the elastic rod inserts in the unit cell. The influences of electrical boundaries (including electric-open, applied electric capacity, electric-short and applied feedback control conditions) on the band structures are investigated to illustrate the active control scheme. From the calculated comprehensive frequency spectra over a large frequency range, the dispersion properties of the characteristic longitudinal waves in rod-type piezoelectric phononic crystals are summarized. Full article
(This article belongs to the Special Issue Phononic Crystals)
Open AccessFeature PaperArticle One-Dimensional Mass-Spring Chains Supporting Elastic Waves with Non-Conventional Topology
Crystals 2016, 6(4), 44; doi:10.3390/cryst6040044
Received: 26 February 2016 / Revised: 4 April 2016 / Accepted: 13 April 2016 / Published: 16 April 2016
Cited by 2 | PDF Full-text (2240 KB) | HTML Full-text | XML Full-text
Abstract
There are two classes of phononic structures that can support elastic waves with non-conventional topology, namely intrinsic and extrinsic systems. The non-conventional topology of elastic wave results from breaking time reversal symmetry (T-symmetry) of wave propagation. In extrinsic systems, energy is injected into
[...] Read more.
There are two classes of phononic structures that can support elastic waves with non-conventional topology, namely intrinsic and extrinsic systems. The non-conventional topology of elastic wave results from breaking time reversal symmetry (T-symmetry) of wave propagation. In extrinsic systems, energy is injected into the phononic structure to break T-symmetry. In intrinsic systems symmetry is broken through the medium microstructure that may lead to internal resonances. Mass-spring composite structures are introduced as metaphors for more complex phononic crystals with non-conventional topology. The elastic wave equation of motion of an intrinsic phononic structure composed of two coupled one-dimensional (1D) harmonic chains can be factored into a Dirac-like equation, leading to antisymmetric modes that have spinor character and therefore non-conventional topology in wave number space. The topology of the elastic waves can be further modified by subjecting phononic structures to externally-induced spatio-temporal modulation of their elastic properties. Such modulations can be actuated through photo-elastic effects, magneto-elastic effects, piezo-electric effects or external mechanical effects. We also uncover an analogy between a combined intrinsic-extrinsic systems composed of a simple one-dimensional harmonic chain coupled to a rigid substrate subjected to a spatio-temporal modulation of the side spring stiffness and the Dirac equation in the presence of an electromagnetic field. The modulation is shown to be able to tune the spinor part of the elastic wave function and therefore its topology. This analogy between classical mechanics and quantum phenomena offers new modalities for developing more complex functions of phononic crystals and acoustic metamaterials. Full article
(This article belongs to the Special Issue Phononic Crystals)
Open AccessArticle Accelerated Approach for the Band Structures Calculation of Phononic Crystals by Finite Element Method
Crystals 2016, 6(1), 11; doi:10.3390/cryst6010011
Received: 22 December 2015 / Revised: 11 January 2016 / Accepted: 12 January 2016 / Published: 14 January 2016
Cited by 2 | PDF Full-text (11017 KB) | HTML Full-text | XML Full-text
Abstract
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
[...] Read more.
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. Full article
(This article belongs to the Special Issue Phononic Crystals)

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