Showing papers on "Dispersion relation published in 2017"
TL;DR: In this paper, the authors consider the canonical problem of an array of rods, which act as resonators, placed on an elastic substrate; the substrate being either a thin elastic plate or an elastic half-space.
Abstract: We consider the canonical problem of an array of rods, which act as resonators, placed on an elastic substrate; the substrate being either a thin elastic plate or an elastic half-space. In both cases the flexural plate, or Rayleigh surface, waves in the substrate interact with the resonators to create interesting effects such as effective band-gaps for surface waves or filters that transform surface waves into bulk waves; these effects have parallels in the field of optics where such sub-wavelength resonators create metamaterials in the bulk and metasurfaces at the free surfaces.
Here we carefully analyse this canonical problem by extracting the dispersion relations analytically thereby examining the influence of both the flexural and compressional resonances on the propagating wave. For an array of resonators atop an elastic half-space we augment the analysis with numerical simulations. Amongst other effects, we demonstrate the striking effect of a dispersion curve which corresponds to a mode that transitions from Rayleigh wave-like to shear wave-like behaviour and the resultant change in the fields from surface to bulk waves.
152 citations
TL;DR: In this article, a global linear stability analysis based on the turbulent mean flow was conducted to identify trapped acoustic waves in the potential core of a high-subsonic jet, which can be unambiguously identified by a local dispersion relation.
Abstract: Coherent features of a turbulent Mach 0.9, Reynolds number 10^6 jet are educed from a high-fidelity large eddy simulation. Besides the well-known Kelvin–Helmholtz instabilities of the shear layer, a new class of trapped acoustic waves is identified in the potential core. A global linear stability analysis based on the turbulent mean flow is conducted. The trapped acoustic waves form branches of discrete eigenvalues in the global spectrum, and the corresponding global modes accurately match the educed structures. Discrete trapped acoustic modes occur in a hierarchy determined by their radial and axial order. A local dispersion relation is constructed from the global modes and found to agree favourably with an empirical dispersion relation educed from the simulation data. The product between direct and adjoint modes is then used to isolate the trapped waves. Under certain conditions, resonance in the form of a beating occurs between trapped acoustic waves of positive and negative group velocities. This resonance explains why the trapped modes are prominently observed in the simulation and as tones in previous experimental studies. In the past, these tones were attributed to external factors. Here, we show that they are an intrinsic feature of high-subsonic jets that can be unambiguously identified by a global linear stability analysis.
120 citations
TL;DR: In this article, spin-wave propagation in Yttrium iron garnet (YIG) waveguides is studied using propagating spin wave spectroscopy (PSWS) and phase resolved micro-focused Brillouin Light Scattering (μ-BLS).
Abstract: Spin-wave propagation in microfabricated 20 nm thick, 25 μm wide Yttrium Iron Garnet (YIG) waveguides is studied using propagating spin-wave spectroscopy (PSWS) and phase resolved micro-focused Brillouin Light Scattering (μ-BLS) spectroscopy We demonstrate that spin-wave propagation in 50 parallel waveguides is robust against microfabrication induced imperfections and extract spin-wave propagation parameters for the Damon-Eshbach configuration in a wide range of excitation frequencies As expected from its low damping, YIG allows for the propagation of spin waves over long distances; the attenuation lengths is 25 μm at μ 0 H = 45 mT Moreover, direct mapping of spin waves by μ-BLS allows us to reconstruct the spin-wave dispersion relation and to confirm the multi-mode propagation in the waveguides, glimpsed by propagating spin-wave spectroscopy
104 citations
TL;DR: In this article, the authors present the equations of relativistic hydrodynamics coupled to dynamical electromagnetic fields, including the effects of polarization, electric fields, and derivative expansion.
Abstract: We present the equations of relativistic hydrodynamics coupled to dynamical electromagnetic fields, including the effects of polarization, electric fields, and the derivative expansion We enumerate the transport coefficients at leading order in derivatives, including electrical conductivities, viscosities, and thermodynamic coefficients We find the constraints on transport coefficients due to the positivity of entropy production, and derive the corresponding Kubo formulas For the neutral state in a magnetic field, small fluctuations include Alfven waves, magnetosonic waves, and the dissipative modes For the state with a non-zero dynamical charge density in a magnetic field, plasma oscillations gap out all propagating modes, except for Alfven-like waves with a quadratic dispersion relation We relate the transport coefficients in the "conventional" magnetohydrodynamics (formulated using Maxwell's equations in matter) to those in the "dual" version of magnetohydrodynamics (formulated using the conserved magnetic flux)
102 citations
TL;DR: In this paper, the dispersion relations and band gaps for the propagation of elastic waves in the undeformed and fully deformed stable configurations were determined using finite element models, and a reduced order model based on a one-dimensional lattice was developed to interpret and explain the emergence of low frequency band gaps in intermediate stable configurations in which some unit cells are undeformed while others are deformed.
99 citations
TL;DR: Through fits to an extensive data set of dispersion relations combined with magnetization measurements, the spin Hamiltonian is reevaluate, finding dominant quantum exchange terms, which are proposed to be responsible for the anomalously strong fluctuations and quasiparticle breakdown effects observed at low fields.
Abstract: The frustrated pyrochlore magnet Yb_{2}Ti_{2}O_{7} has the remarkable property that it orders magnetically but has no propagating magnons over wide regions of the Brillouin zone. Here we use inelastic neutron scattering to follow how the spectrum evolves in cubic-axis magnetic fields. At high fields we observe, in addition to dispersive magnons, a two-magnon continuum, which grows in intensity upon reducing the field and overlaps with the one-magnon states at intermediate fields leading to strong renormalization of the dispersion relations, and magnon decays. Using heat capacity measurements we find that the low- and high-field regions are smoothly connected with no sharp phase transition, with the spin gap increasing monotonically in field. Through fits to an extensive data set of dispersion relations combined with magnetization measurements, we reevaluate the spin Hamiltonian, finding dominant quantum exchange terms, which we propose are responsible for the anomalously strong fluctuations and quasiparticle breakdown effects observed at low fields.
98 citations
TL;DR: In this article, the wave propagation of size-dependent functionally graded (FG) nanobeams resting on elastic foundation subjected to axial magnetic field based on the nonlocal strain gradient theory and Euler-Bernoulli beam model was investigated by using an analytical approach.
Abstract: This paper investigates wave propagation of size-dependent functionally graded (FG) nanobeams resting on elastic foundation subjected to axial magnetic field based on the nonlocal strain gradient theory and Euler–Bernoulli beam model by using an analytical approach. The nonlocal beam model has a length scale parameter and captures the size influences. Material properties are spatially graded according to sigmoid distribution. A derivation of the governing equations for the wave propagation analysis of nanoscale S-FGM beams is conducted. Then, the dispersion relations between wave frequency and phase velocity with the wave number is investigated. It is found that wave propagation characteristics of nonlocal S-FGM beams are influenced by various parameters including length scale parameter, material graduation, elastic foundation parameters and magnetic field intensity.
90 citations
TL;DR: In this article, the dispersion relation of pure-magnetostatic wave was observed in a table-top all-optical spectroscopy named spin-wave tomography.
Abstract: To know the properties of a particle or a wave, one should measure how its energy changes with its momentum. The relation between them is called the dispersion relation, which encodes essential information of the kinetics. In a magnet, the wave motion of atomic spins serves as an elementary excitation, called a spin wave, and behaves like a fictitious particle. Although the dispersion relation of spin waves governs many of the magnetic properties, observation of their entire dispersion is one of the challenges today. Spin waves whose dispersion is dominated by magnetostatic interaction are called pure-magnetostatic waves, which are still missing despite of their practical importance. Here, we report observation of the band dispersion relation of pure-magnetostatic waves by developing a table-top all-optical spectroscopy named spin-wave tomography. The result unmasks characteristics of pure-magnetostatic waves. We also demonstrate time-resolved measurements, which reveal coherent energy transfer between spin waves and lattice vibrations.
86 citations
TL;DR: In this article, two wave modes for the integrable fifth-order Korteweg-de Vries (TfKdV) equations were established and necessary conditions of the nonlinearity and dispersion parameters of the equation for multiple-soliton solutions to exist.
Abstract: In this work we establish two wave modes for the integrable fifth-order Korteweg-de Vries (TfKdV) equations. We determine necessary conditions of the nonlinearity and dispersion parameters of the equation for multiple-soliton solutions to exist. We apply the simplified Hirota method to derive multiple-soliton solutions under these conditions. We also examine the dispersion relations and the phase shifts of the developed models.
79 citations
TL;DR: Numerical results show that, the formation mechanism of opening the low‐frequency band gap is attributed to the coupling between the local resonant Lamb modes of two‐dimensional phononic plate and the resonant modes of the stepped resonators.
72 citations
TL;DR: In this paper, the authors derived analytical expressions for the IA-wave dispersion relation in an anisotropic plasma in the framework of gyrokinetics and then compared them to fully kinetic numerical calculations, results from two-fluid theory, and magnetohydrodynamics (MHD).
Abstract: Observations in the solar wind suggest that the compressive component of inertial-range solar-wind turbulence is dominated by slow modes. The low collisionality of the solar wind allows for nonthermal features to survive, which suggests the requirement of a kinetic plasma description. The least-damped kinetic slow mode is associated with the ion-acoustic (IA) wave and a nonpropagating (NP) mode. We derive analytical expressions for the IA-wave dispersion relation in an anisotropic plasma in the framework of gyrokinetics and then compare them to fully kinetic numerical calculations, results from two-fluid theory, and magnetohydrodynamics (MHD). This comparison shows major discrepancies in the predicted wave phase speeds from MHD and kinetic theory at moderate to high β. MHD and kinetic theory also dictate that all plasma normal modes exhibit a unique signature in terms of their polarization. We quantify the relative amplitude of fluctuations in the three lowest particle velocity moments associated with IA and NP modes in the gyrokinetic limit and compare these predictions with MHD results and in situ observations of the solar-wind turbulence. The agreement between the observations of the wave polarization and our MHD predictions is better than the kinetic predictions, which suggests that the plasma behaves more like a fluid in the solar wind than expected.
TL;DR: In this article, the authors prove wave breaking in the nonlinear nonlocal equation which combines the dispersion relation of water waves and a nonlinearity of the shallow water equations, provided that the slope of the initial datum is sufficiently negative.
TL;DR: In this article, the dispersion properties of a state-based linear peridynamic solid model were investigated and the role of the horizon was investigated, where the authors showed how the influence function can be used to minimize wave dispersion at a fixed lattice spacing and demonstrate it qualitatively by wave propagation analysis in one-and two-dimensional models of elastic solids.
Abstract: Peridynamics is a nonlocal continuum model which offers benefits over classical continuum models in cases, where discontinuities, such as cracks, are present in the deformation field. However, the nonlocal characteristics of peridynamics leads to a dispersive dynamic response of the medium. In this study we focus on the dispersion properties of a state-based linear peridynamic solid model and specifically investigate the role of the peridynamic horizon. We derive the dispersion relation for one, two and three dimensional cases and investigate the effect of horizon size, mesh size (lattice spacing) and the influence function on the dispersion properties. We show how the influence function can be used to minimize wave dispersion at a fixed lattice spacing and demonstrate it qualitatively by wave propagation analysis in one- and two-dimensional models of elastic solids. As a main contribution of this paper, we propose to associate peridynamic non-locality expressed by the horizon with a characteristic length scale related to the material microstructure. To this end, the dispersion curves obtained from peridynamics are compared with experimental data for two kinds of sandstone.
TL;DR: In this article, a three-layered plate with high-contrast mechanical and geometric properties of the layers is analyzed and two-mode asymptotic polynomial expansions of the Rayleigh-Lamb dispersion relation approximating both the fundamental bending wave and the first harmonic are derived.
TL;DR: In this article, the authors show that velocities of the asymmetric solitary wave with asymmetric bipolar parallel electric field are close to velocity of electron-acoustic waves (existing due to the presence of cold and hot electrons) and follow the Korteweg-de Vries dispersion relation derived for the observed plasma conditions.
Abstract: The Van Allen Probes observe generally two types of electrostatic solitary waves (ESW) contributing to the broadband electrostatic wave activity in the nightside inner magnetosphere. ESW with symmetric bipolar parallel electric field are electron phase space holes. The nature of ESW with asymmetric bipolar (and almost unipolar) parallel electric field has remained puzzling. To address their nature, we consider a particular event observed by Van Allen Probes to argue that during the broadband wave activity electrons with energy above 200 eV provide the dominant contribution to the total electron density, while the density of cold electrons (below a few eV) is less than a few tenths of the total electron density. We show that velocities of the asymmetric ESW are close to velocity of electron-acoustic waves (existing due to the presence of cold and hot electrons) and follow the Korteweg-de Vries (KdV) dispersion relation derived for the observed plasma conditions (electron energy spectrum is a power law between about 100 eV and 10 keV and Maxwellian above 10 keV). The ESW spatial scales are in general agreement with the KdV theory. We interpret the asymmetric ESW in terms of electron-acoustic solitons and double layers (shocks waves).
TL;DR: In this paper, the authors show that due to linear energy dispersion, the traditional thermionic emission and field emission models are no longer valid for graphene and two-dimensional Dirac-like materials.
Abstract: The theories of thermionic emission and field emission (also known as the Richardson–Dushman [RD] and Fowler–Nordheim [FN] Laws, respectively) were formulated more than 80 years ago for bulk materials. In single-layer graphene, electrons mimic massless Dirac fermions and follow relativistic carrier dynamics. Thus, their behavior deviates significantly from the nonrelativistic electrons that reside in traditional bulk materials with a parabolic energy-momentum dispersion relation. In this article, we assert that due to linear energy dispersion, the traditional thermionic emission and field emission models are no longer valid for graphene and two-dimensional Dirac-like materials. We have proposed models that show better agreement with experimental data and also show a smooth transition to the traditional RD and FN Laws.
TL;DR: In this paper, the authors derived a formula for the contribution of drift motion of phonons to total heat flux at steady state and showed that phonon flow can be reasonably approximated as hydrodynamic if the SWCNT is long enough to avoid ballistic phonon transport.
Abstract: Two hydrodynamic features of phonon transport, phonon drift and second sound, in a (20,20) single-wall carbon nanotube (SWCNT) are discussed using lattice dynamics calculations employing an optimized Tersoff potential for atomic interactions We formally derive a formula for the contribution of drift motion of phonons to total heat flux at steady state It is found that the drift motion of phonons carries more than $70%$ and $90%$ of heat at 300 and 100 K, respectively, indicating that phonon flow can be reasonably approximated as hydrodynamic if the SWCNT is long enough to avoid ballistic phonon transport The dispersion relation of second sound is derived from the Peierls-Boltzmann transport equation with Callaway's scattering model and quantifies the speed of second sound and its relaxation The speed of second sound is around 4000 m/s in a (20,20) SWCNT and the second sound can propagate more than 10 \textmu{}m in an isotopically pure (20,20) SWCNT for frequency around 1 GHz at 100 K
TL;DR: In this paper, wave dispersion behavior of a temperature-dependent functionally graded (FG) nanobeam undergoing rotation subjected to thermal loading is investigated according to nonlocal strain gradient theory, in which the stress enumerates for both nonlocal stress field and the strain gradient stress field.
Abstract: In the present article, wave dispersion behavior of a temperature-dependent functionally graded (FG) nanobeam undergoing rotation subjected to thermal loading is investigated according to nonlocal strain gradient theory, in which the stress enumerates for both nonlocal stress field and the strain gradient stress field. Mori–Tanaka distribution model is considered to express the gradual variation of material properties across the thickness. The governing equations are derived as a function of axial force due to centrifugal stiffening and displacements by applying Hamilton’s principle according to Euler–Bernoulli beam theory. By applying an analytical solution, the dispersion relations of rotating FG nanobeam are obtained by solving an eigenvalue problem. Obviously, numerical results indicate that various parameters such as angular velocity, gradient index, temperature change, wave number, and nonlocality parameter have significant influences on the wave characteristics of rotating FG nanobeams. Hen...
TL;DR: By combining Brillouin light scattering and micromagnetic simulations, the authors studied the spin-wave dynamics of a Co/Pd thin film multilayer, which features a stripe domain structure at remanence.
Abstract: By combining Brillouin light scattering and micromagnetic simulations, we studied the spin-wave (SW) dynamics of a Co/Pd thin film multilayer, which features a stripe domain structure at remanence. The periodic up and down domains are separated by corkscrew type domain walls. The existence of these domains causes a scattering of the otherwise bulk and surface SW modes, which form mode families, similar to a one-dimensional magnonic crystal. The dispersion relation and mode profiles of SWs are measured for the transferred wave vector parallel and perpendicular to the domain axis.
TL;DR: It is demonstrated that tuning can be achieved by modifying the Fermi energy and tunability of the graphene-dielectric heterostructures can be enhanced further by changing either the thickness of the dielectric layers or the number of graphene sheets employed.
Abstract: Despite the fact that metal is the most common conducting constituent element in the fabrication of metamaterials, one of the advantages of graphene over metal is that its conductivity can be controlled by the Fermi energy. Here, we theoretically investigate multilayer structures comprising alternating graphene and dielectric layers as a class of hyperbolic metamaterials for THz frequencies based on a general simple model of the graphene and the dielectric layers. By employing a method of matching the tangential components of the electrical and magnetic fields, we derive the relevant dispersion relations and demonstrate that tuning can be achieved by modifying the Fermi energy. Moreover, tunability of the graphene-dielectric heterostructures can be enhanced further by changing either the thickness of the dielectric layers or the number of graphene sheets employed. Calculated dispersion relations, propagation lengths of plasmon modes in the system are presented. This allows us to characterize and categorize the modes into two groups: Ferrel-Berreman modes and surface plasmon polaritons.
TL;DR: It is reported that in an in-plane magnetised magnetic film the in- plane direction of a propagating spin wave can be changed by up to 90 degrees using an externally induced magnetic gradient field.
Abstract: Spin waves are of large interest as data carriers for future logic devices. However, due to the strong anisotropic dispersion relation of dipolar spin-waves in in-plane magnetised films the realisation of two-dimensional information transport remains a challenge. Bending of the energy flow is prohibited since energy and momentum of spin waves cannot be conserved while changing the direction of wave propagation. Thus, non-linear or non-stationary mechanisms are usually employed. Here, we propose to use reconfigurable laser-induced magnetisation gradients to break the system's translational symmetry. The resulting changes in the magnetisation shift the dispersion relations locally and allow for operating with different spin-wave modes at the same frequency. Spin-wave momentum is first transformed via refraction at the edge of the magnetisation gradient region and then adiabatically modified inside it. Along these lines the spin-wave propagation direction can be controlled in a broad frequency range with high efficiency.
TL;DR: In this paper, the authors proposed a real physical system, the honeycomb lattice, as a possible realization of the fractional Schrodinger equation (FSE) system, through utilization of the Dirac-Weyl equation (DWE).
Abstract: We suggest a real physical system — the honeycomb lattice — as a possible realization of the fractional Schrodinger equation (FSE) system, through utilization of the Dirac-Weyl equation (DWE). The fractional Laplacian in FSE causes modulation of the dispersion relation of the system, which becomes linear in the limiting case. In the honeycomb lattice, the dispersion relation is already linear around the Dirac point, suggesting a possible connection with the FSE, since both models can be reduced to the one described by the DWE. Thus, we propagate Gaussian beams in three ways: according to FSE, honeycomb lattice around the Dirac point, and DWE, to discover universal behavior — the conical diffraction. However, if an additional potential is brought into the system, the similarity in behavior is broken, because the added potential serves as a perturbation that breaks the translational periodicity of honeycomb lattice and destroys Dirac cones in the dispersion relation.
TL;DR: In this article, the authors apply Fourier filtering, in both spatial and temporal domains, to extract chromospheric umbral wave characteristics consistent with an m=1 slow magneto-acoustic mode.
Abstract: Solar chromospheric observations of sunspot umbrae offer an exceptional view of magneto-hydrodynamic wave phenomena In recent years, a wealth of wave signatures related to propagating magneto-acoustic modes have been presented, which demonstrate complex spatial and temporal structuring of the wave components Theoretical modelling has demonstrated how these ubiquitous waves are consistent with an m=0 slow magneto-acoustic mode, which are excited by trapped sub-photospheric acoustic (p-mode) waves However, the spectrum of umbral waves is broad, suggesting that the observed signatures represent the superposition of numerous frequencies and/or modes We apply Fourier filtering, in both spatial and temporal domains, to extract chromospheric umbral wave characteristics consistent with an m=1 slow magneto-acoustic mode This identification has not been described before Angular frequencies of 0037 +/- 0007 rad/s (21 +/- 04 deg/s), corresponding to a period approximately 170 s for the m=1 mode are uncovered for spatial wavenumbers in the range of 045
TL;DR: In this paper, the authors derived the equations of wave motion based on the nonlocal piezoelectricity continuum theory, and the symmetric wave mode was considered, where the dispersion relation was obtained to analyze the behavior of the guided elastic waves and the influences of the nanoscale size-effect.
Abstract: This paper is concerned with the guided elastic waves propagating in nanoscale layered periodic piezoelectric composites. The equations of wave motion based on the nonlocal piezoelectricity continuum theory are derived, and the symmetric wave mode is considered. According to the continuity conditions of the mechanical and electric field quantities on the interface between the two neighboring sub-layers, we obtain the dispersion relation to analyze the behavior of the guided elastic waves and the influences of the nanoscale size-effect. A cut-off frequency appears when taking the nanoscale size-effect into consideration. The variations of the mechanical displacements and the electrical potential are calculated and discussed. The influences of the nanoscale size-effect and the volume fractions on the mode conversions are analyzed in details. It is found that all the dispersion curves including the mode conversion zones are compressed under the cut-off frequency. As the ratio of the internal to external characteristic lengths increases, the cut-off frequency decreases, while the frequency and the wave number of the mode conversion reduce. The present investigation may help us to control the cut-off frequency and the mode conversions by tuning the internal or external characteristic lengths and the volume fractions of the nanoscale layered periodic piezoelectric composites. The corresponding results may provide the theoretical basis for nanoscale wave device applications to control the wave mode conversions and the cut-off frequency.
TL;DR: Wentzel-Kramers-Brillouin approximation technique is used to find the particle displacements due to surface wave propagation in bedded structure with distinct material properties as discussed by the authors.
Abstract: Wentzel–Kramers–Brillouin approximation technique serves as a powerful tool to find the particle displacements due to surface wave propagation in bedded structure with distinct material properties
TL;DR: In this paper, a constitutive equation and a governing equation for in-plane wave propagation in viscoelastic monolayer graphene were developed by employing Hamilton's principle and nonlocal strain gradient theory.
Abstract: The behaviors of monolayer graphene sheet have attracted increasing attention of many scientists and researchers. In this study, the propagation behaviors of in-plane wave in viscoelastic monolayer graphene are investigated. The constitutive equation and governing equation for in-plane wave propagation is developed by employing Hamilton’s principle and nonlocal strain gradient theory. By solving the governing equation of motion, the closed-form dispersion relation between phase velocity and wave number is derived and an asymptotic phase velocity can be acquired. The effects of wave number, material length scale parameter, nonlocal parameter and damping coefficient on in-plane wave propagation behaviors are discussed in the numerical studies. It is found that, when exciting wavelengths or structural dimensions become comparable to the material length scale parameters and nonlocal parameters, the scaling effects on wave propagation behaviors are significant. For nanoscaled graphene sheet, the effects of nonlocal parameter, material length scale parameter and damping coefficient on phase velocity are tiny at low wave numbers while significant at high wave numbers. The phase velocity would increase with the increase of material length scale parameter or the decrease of nonlocal parameter and damping coefficient. Furthermore, results indicate that the asymptotic phase velocity can be increase by increasing material length scale parameter or decreasing nonlocal parameter.
TL;DR: In this article, the authors derived long wave estimates for phase and group velocities of the shear waves propagating in any direction in DE laminates subjected to any homogenous deformation in the presence of an electric filed.
Abstract: We analyze small amplitude shear waves propagating in dielectric elastomer (DE) laminates subjected to finite deformations and electrostatic excitations. First, we derive long wave estimates for phase and group velocities of the shear waves propagating in any direction in DE laminates subjected to any homogenous deformation in the presence of an electric filed. To this end, we utilize a micromechanics based energy potential for layered media with incompressible phases described by neo-Hookean ideal DE model. The long wave estimates reveal the significant influence of electric field on the shear wave propagation. However, there exists a configuration, for which electric field does not influence shear waves directly, and can only alter the shear waves through deformation. We study this specific configuration in detail, and derive an exact solution for the steady-state small amplitude waves propagating in the direction perpendicular to the finitely deformed DE layers subjected to electrostatic excitation. In agreement with the long wave estimate, the exact dispersion relation and the corresponding shear wave band gaps (SBGs) – forbidden frequency regions – are not influenced by electric field. However, SBGs in DE laminates with highly nonlinear electroelastic phases still can be manipulated by electric field through electrostatically induced deformation. In particular, SBGs in DE laminates with electroelastic Gent phases widen and shift towards higher frequencies under application of an electric field perpendicular to the layers. However, in laminates with neo-Hookean ideal DE phases, SBGs are not influenced either by electric field or by deformation. This is due to the competing mechanisms of two governing factors: changes in geometry and material properties induced by deformation. In this particular case, these two competing factors entirely cancel each other.
TL;DR: In this paper, the degenerate band edge (DBE) condition was observed in loaded circular metallic waveguides, where four Bloch modes, two propagating and two evanescent, coalesce at a single frequency.
Abstract: We experimentally demonstrate for the first time the degenerate band edge (DBE) condition, namely, the degeneracy of four Bloch modes, in loaded circular metallic waveguides. The four modes forming the DBE represent a degeneracy of the fourth order occurring in a periodic structure where four Bloch modes, two propagating and two evanescent, coalesce. The DBE is associated with four Bloch eigenmodes representing wave propagation in the periodic structure that coalesce in both wavenumbers and eigenvectors (i.e., polarizations), at a single frequency. It leads to a very flat wavenumber-frequency dispersion relation, and the finite-length structure’s quality factor scales as $N^{5}$ , where $N$ is the number of unit cells. The proposed waveguide in which DBE is observed here is designed by periodically loading a circular waveguide with misaligned elliptical metallic rings. We validate the existence of the DBE in such structure using measurements, and we report good agreement between full-wave simulation and the measured response of the waveguide near the DBE frequency; taking into account metallic losses. We correlate our finding to theoretical and simulation results utilizing various techniques, including dispersion synthesis, and scaling of the quality factor and group delay with length. Moreover, the reported geometry is only an example of metallic waveguide with DBE: DBE and its characteristics can also be designed in many other kinds of waveguides and various applications can be contemplated as high-power microwave generation in amplifiers and oscillators based on an electron beam interaction or solid-state devices, pulse compressors, and microwave sensors.
TL;DR: In this paper, the dispersion behavior of waves in magneto-electro-elastic (MEE) nanobeams was investigated based on the nonlocal theory by using the Hamilton's principle.
Abstract: This paper makes the first attempt to investigate the dispersion behavior of waves in magneto-electro-elastic (MEE) nanobeams The Euler nanobeam model and Timoshenko nanobeam model are developed in the formulation based on the nonlocal theory By using the Hamilton’s principle, we derive the governing equations which are then solved analytically to obtain the dispersion relations of MEE nanobeams Results are presented to highlight the influences of the thermo-electro-magnetic loadings and nonlocal parameter on the wave propagation characteristics of MEE nanobeams It is found that the thermo-electro-magnetic loadings can lead to the occurrence of the cut-off wave number below which the wave can’t propagate in MEE nanobeams
TL;DR: In this paper, the propagation of surface waves in both one-and two-dimensional periodic structures is investigated and an energy distribution parameter is defined and a new method for identifying surface wave modes is suggested.