Plane Wave Propagation Research Articles

Absorption measurements—A never ending story?!

A brief historical review on measurement techniques of sound absorption or the acoustic surface impedance will be presented, starting from procedures in the 1930s. Many in situ and laboratory methods have been described over the years. Most of these methods are based on the assumption of plane wave propagation or diffuse sound field. Measurement examples will be shown for some of the methods presented and compared to each other. A commonly used measurement procedure of so-called diffuse sound absorption coefficients is described in the international standard ISO 354. The present revision of the standard only focuses on the conditioning of the sound field and further applying Sabine equation. A diffuse sound field is atheoretical approach. Geometrical acoustics as the basis of sound field simulation has been applied to measurements in a virtual reverberation chamber on absorber baffle set-ups [see Probst (2015)] and showed good agreement between measured and calculated values. This approach is used to investigate the effect of sample size and sample position. Correspondingly, non-standard measurements are compared with simulation results.

DEH Scheme DGTD-Based Transient Modeling Approach for the Cole–Cole Dispersive Media Using Tustin’s Method

The Cole–Cole model can simulate the electromagnetic properties of biological tissues more accurately in a wide frequency band. The current simulation of wave propagation in the Cole–Cole dispersive media usually uses the finite-difference time-domain (FDTD) method, but its requirements in small grid size and time step interval for curved objects limit its application in calculating multiscale complex biological tissues. The discontinuous Galerkin time-domain (DGTD) method is more suitable for simulating multiscale complex targets because it can use unstructured grids and high-order basis functions. Therefore, this article proposes a transient modeling approach for the Cole–Cole dispersive media based on DGTD method, in which the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$z$ </tex-math></inline-formula> transform is performed on the Cole–Cole model, and the fractional power terms are approximated to integer power polynomials according to the continued fraction theory. Moreover, in order to avoid the frequency-dependent permittivity in Maxwell’s equations, the DEH scheme is constructed and a weak form equation for the constitutive relationship between D and E is created. Maxwell’s equations and the constitutive relationship are updated by the leap-frog time-stepping method. The accuracy and ability of the new method are verified by simulating the plane wave propagation in various Cole–Cole media.

Controlling cylindrical waves using effective phononic crystals

Phononic crystals (PCs) are periodic media that can exhibit novel wave propagation behaviors. The analysis of PCs relies on the Bloch theorem, and the application of which implies that certain canonical behaviors can be supported, e.g., band gaps. The Bloch theorem assumes plane wave propagation; however, this is not always the case, e.g., for cylindrical or spherical wave fronts. Here, we redefine material properties in PCs in the presence of cylindrically propagating waves, such that the resulting wave equations contain periodic coefficients. In this sense, an equivalent system can be defined on which Bloch theorem can be applied to predict its wave response. This talk will discuss our recent work on effective phononic crystals, which are PCs that are not geometrically periodic but whose material properties result in periodic coefficients in the wave equation. We demonstrate these concepts using radially-propagating torsional waves and use finite element method models to solve for material properties that result in Bragg scattering-based band gaps, locally resonant band gaps, and topologically protected interface modes. Finally, we conduct experimental validations on 3D printed samples fabricated with multi-material polyjet printing. This work has applications to mitigating damaging torsional vibrations in rotating machinery such as turbines, compressors, and engines.

Enantioselective optical gradient forces using 3D structured vortex light

Here we highlight enantioselective optical gradient forces present in 3D (non-paraxial) structured optical vortex tweezing systems. One chiral force originates from the circular polarization of the light, while remarkably the other is independent of the input polarization - even occurring for unpolarized light – and is not present in 2D structured light nor propagating plane waves. This latter chiral sorting mechanism allows for the enantioselective trapping of chiral particles into distinct rings in the transverse plane through conservative radial forces.

A Mathematical Model for Electrical Activity in Pig Atrial Tissue.

State of the art mathematical models are currently used to bridge the gap between basic research conducted in the laboratory and preclinical research conducted on large animals, which ultimately paves the way for clinical translation. In this regard, there is a great need for models that can be used alongside experiments for in-depth investigation and validation. One such experimental model is the porcine atrium, which is commonly used to study the mechanisms of onset and control of atrial fibrillation in the context of its surgical management. However, a mathematical model of pig atria is lacking. In this paper, we present the first ionically detailed mathematical model of porcine atrial electrophysiology, at body temperature. The model includes 12 ionic currents, 4 of which were designed based on experimental patch-clamp data directly obtained from literature. The formulations for the other currents are adopted from the human atrial model, and modified for porcine specificity based on our measured restitution data for different action potential characteristics: resting membrane potential, action potential amplitude, maximum upstroke velocity and action potential duration and different levels of membrane voltage repolarization. The intracellular Ca2+ dynamics follows the Luo-Rudy formulation for guinea pig ventricular cardiomyocytes. The resulting model represents “normal” cells which are formulated as a system of ordinary differential equations. We extend our model to two dimensions to obtain plane wave propagation in tissue with a velocity of 0.58 m/s and a wavelength of 8 cm. The wavelength reduces to 5 cm when the tissue is paced at 200 ms. Using S1-S2 cross-field protocol, we demonstrate in an 11.26 cm square simulation domain, the ability to initiate single spiral waves (rotation period ≃ 180 ms) that remain stable for more than 40 s. The spiral tip exhibits hypermeander. In agreement with previous experimental results using pig atria, our model shows that early repolarization is primarily driven by a calcium-mediated chloride current, IClCa, which is completely inactivated at high pacing frequencies. This is a condition that occurs only in porcine atria. Furthermore, the model shows spatiotemporal chaos with reduced repolarization.

Silencer for high-frequency turbocharger compressor noise via an acoustic straightener

Decades of successful research and development on automotive silencers for engine breathing systems have brought about significant reductions in emitted engine noise. A majority of this research has pursued airborne noise at relatively low frequencies, which typically involves planar wave propagation. However, with the increasing demand for downsized turbocharged engines in passenger cars, high-frequency compressor noise has become a challenge in engine induction systems. Elevated frequencies promote multi-dimensional wave propagation rendering at times conventional silencer treatments ineffective due to the underlying assumption of one-dimensional wave propagation in their design. The present work focuses on developing a high-frequency silencer that targets tonal noise at the blade-pass frequency within the compressor inlet duct for a wide range of rotational speeds. The approach features a novel "acoustic straightener" that creates exclusive planar wave propagation near the silencing elements. An analytical treatment is combined with three-dimensional (3D) acoustic finite element method to guide the early design process. The effects of mean flow and nonlinearities on acoustics are captured by 3D computational fluid dynamics (CFD) simulations which are then utilized to introduce geometry modifications that reduce flow losses and suppress noise generation due to flow-acoustic coupling. The effectiveness of the silencer in the presence of mean flow is demonstrated by computing the transmission loss across the configuration from 3D CFD predictions.

Acoustoelastic analysis of soft viscoelastic solids with application to pre-stressed phononic crystals

The effective dynamic properties of specific periodic structures involving rubber-like materials can be adjusted by pre-strain, thus facilitating the design of custom acoustic filters. While nonlinear viscoelastic behaviour is one of the main features of soft solids, it has been rarely incorporated in the study of such phononic media. Here, we study the dynamic response of nonlinear viscoelastic solids within a ‘small-on-large’ acoustoelasticity framework, that is we consider the propagation of small amplitude waves superimposed on a large static deformation. Incompressible soft solids whose behaviour is described by the Fung–Simo quasi-linear viscoelasticity theory (QLV) are considered. We derive the incremental equations using stress-like memory variables governed by linear evolution equations. Thus, we show that wave dispersion follows a strain-dependent generalised Maxwell rheology. Illustrations cover the propagation of plane waves under homogeneous tensile strain in a QLV Mooney–Rivlin solid. The acoustoelasticity theory is then applied to phononic crystals involving a lattice of hollow cylinders, by making use of a dedicated perturbation approach. In particular, results highlight the influence of viscoelastic dissipation on the location of the first band gap. We show that dissipation shifts the band gap frequencies, simultaneously increasing the band gap width. These results are relevant to practical applications of soft viscoelastic solids subject to static pre-stress.

Reflection of plane waves at the free surface of a magneto-thermoelastic medium with variable thermal conductivity and variable mass diffusivity

The present article deals with the propagation of plane waves in a magneto-thermoelastic medium under the effects of variable thermal conductivity and variable mass diffusivity. It is observed that three coupled longitudinal plane waves and one transverse wave travel in the medium with distinct speeds. The formulae for amplitude ratios and energy ratios corresponding to various reflected waves have been presented, when a set of coupled waves strikes obliquely at the boundary surface of the assumed model. To illustrate the analytical developments, the numerical solution is performed for a particular material and the results in respect of phase velocities, amplitude ratios and energy ratios are presented graphically. It is observed that the results depend upon the angle of incidence, frequency and the thermoelastic properties of the half-space. It is verified that during reflection phenomena, the sum of energy ratios is equal to unity at each angle of incidence and there is no energy dissipation at the free plane boundary. Results of some earlier workers have been deduced from the present formulation.

Pixel-Oriented Adaptive Apodization for Plane-Wave Imaging Based on Recovery of the Complete Dataset.

In theory, coherent plane-wave compounding (CPWC) enables ultrafast ultrasound imaging while maintaining a high imaging quality that is comparable to conventional B-mode imaging based on focused beam transmissions. However, in practice, due to the imperfect synthetization of transmit focusing (e.g., heterogeneous speed of sound in tissue and limited range of steering angle), CPWC suffers from a variety of imaging artifacts resulting from side lobes, grating lobes, and axial lobes. This study focuses on addressing the issues of axial lobes for CPWC, which constitutes an important source of clutter that leads to the degradation of contrast ratio and contrast-to-noise ratio (CR and CNR) of CPWC. We first investigated the source of the axial lobes based on plane-wave propagation and the delay-and-sum (DAS) beamforming. We then proposed a new method that is based on pixel-oriented adaptive apodization (POAA) to eliminate the axial lobes throughout the entire field of view (FOV). POAA was first validated in a simulation study, followed by in vitro phantom experiments and an in vivo case study on a carotid artery from a healthy volunteer. In the simulation study, suppression of axial lobes by 120 dB was observed from wire targets, and an improvement of CNR by up to 60% was found in a cyst-mimicking digital phantom. In the phantom experiment, POAA showed an improvement in CNR by around 20% over conventional methods. The effectiveness of axial lobe suppression was finally demonstrated in vivo, where POAA showed a substantial suppression of clutters throughout the entire FOV.

On wave propagation and free vibration of piezoelectric sandwich plates with perfect and porous functionally graded substrates

This paper aims to develop analytical solutions for wave propagation and free vibration of perfect and porous functionally graded (FG) plate structures integrated with piezoelectric layers. The effect of porosities, which occur in FG materials, is rarely reported in the literature of smart FG plates but included in the present modeling. The modified rule of mixture is therefore considered for variation of effective material properties within the FG substrate. Based on a four-variable higher-order theory, the electromechanical model of the system is established through the use of Hamilton’s principle, and Maxwell’s equation. This theory drops the need of any shear correction factor, and results in less governing equations compared to the conventional higher-order theories. Analytical solutions are applied to the obtained equations to extract the results for two investigations: (I) the plane wave propagation of infinite smart plates and (II) the free vibration of smart rectangular plates with different boundary conditions. After verifying the model, extensive numerical results are presented. Numerical results demonstrate that the wave characteristics of the system, including wave frequency and phase velocity along with the natural frequencies of its bounded counterpart, are highly influenced by the plate parameters such as power-law index, porosity, and piezoelectric characteristics.

Anisotropic elastic parameter estimation from multicomponent ground-motion observations: a theoretical study

SUMMARY We investigate the potential of multicomponent, single-point ground-motion observations (displacement, rotation and strain) to allow the estimation of near-receiver anisotropic elastic parameters. Based on full-space, plane-wave propagation analysis, we demonstrate that in (locally homogeneous) anisotropic media, the wave propagation direction and the velocities of quasi-P and quasi-S waves can—in principle—be determined from three components of displacements and three components of rotations. Mimicking the situation of a borehole setting, we formulate an inverse problem, estimating the full elastic tensor from multidirectional observations. We show that in the presence of noise it is beneficial to observe additionally a longitudinal strain component (e.g. along the borehole), further constraining the predominantly quasi-P related elastic tensor components.

On the Propagation of Plane Waves in Three-Dimensional Cubic Quasicrystal Nanoplates with Surface Effects

On the Propagation of Plane Waves in Three-Dimensional Cubic Quasicrystal Nanoplates with Surface Effects

Analysis, Sources and Study of the Biological Consequences of Electromagnetic Pollution

The actions and health effects of electromagnetic fields in the radio frequency (RF) domains, referred to as radio frequencies and HV transmission networks have been studied for several decades. Following the appearance of questions and debates within the population, the actions and potential effects of radiofrequency and HV transport networks on health, in connection with the development of new wireless technologies, are generating a certain revival of interest. Thus, the increasing exposure to electromagnetic fields and the concerns of the public have led health organizations to undertake large-scale research programs to respond to the concerns expressed. These research programs have contributed to significantly increasing the number of studies on the actions and effects of electromagnetic pollution as well as their consequences on living beings. The objective of our research is focused on the analysis, sources, and study of the biological consequences of electromagnetic pollution. To do this, we have used physical laws and theorems, in particular Maxwell-Ampère, Maxwell-Gauss, Maxwell-Faraday, and Ohm’s law, to model the interactions between electromagnetic fields and living matter. In this article we have chosen the approach based on the electrical model of human biological tissue, taking into account on the one hand the physical phenomena of the propagation of an electromagnetic microwave plane wave in the range from 0 to 300GHz and on the other hand, the experimental values to simulate the relaxations α, β and γ and the impedance of the biological tissue faced with the variation of the frequency of propagation of the electromagnetic waves to identify the biological consequences relating thereto. The results obtained in the literature show the linear dependence of bio-impedance on frequency, these observations suggest that the tissue can be physiologically stressed at high frequencies. This can cause biological consequences for humans. The 2D simulation based on the proposed model has been developed as well as the verification of the consistency of the different mathematical models, by comparing the fractal dimensions of the results of the program with those of the figures obtained experimentally.

Compact Antenna Test Range Using Very Small F/D Transmitarray Based on Amplitude Modification and Phase Modulation

A very small focal-to-diameter (F/D) ratio transmitarray for compact antenna test range (CATR) application is proposed in this article. The transmitarray comprises a feed antenna, a metasurface for phase modulation (MPM), and another one for amplitude modification (MAM). MPM and MAM are implemented using the same metasurface cell but with different cell selections and arrangements. A holistic phase-only design method determines whether the metasurface is for amplitude modification or phase modulation. A CATR collimator with an overall low profile is realized through the joint design of MAM and MPM. The proposed technique overcomes the limits of the ordinary metasurface lenses and enables plane wave generation with a short focal length and sizeable quiet zone. The resulting CATR demonstrates a 50% quiet zone of the aperture size with ±0.5-dB amplitude and ±5° phase errors by full-wave simulation. For further verification, a prototype is fabricated, and its experimental results confirm the simulations.

Two-station analysis of passive surface waves with continuous wavelet transform and plane-wave-based beamforming

Using the cross-correlation or cross-coherence method to extract the traveltime information of surface waves between two stations from the ambient noise seismic data has become a popular method, which is widely utilized in shallow, regional, and global-scale geophysical surveys. Different from the common-used narrow-band filter (NBF), we adopt the continuous wavelet transform (CWT) as an alternative method to measure the phase velocity from the interstation cross-correlation function (CCF). On account of the distribution of urban noisy sources it is hard to satisfy the requirement of random, stable, uncorrelated, and uniform, which usually makes the measured phase-velocity uncertain. For those surveys with an ultra-short recording time of noise, the adverse effect would be more severe. Hence, we propose to adopt the plane-wave-based beamforming (PWBB) to scan the incoming direction of surface waves based on the hypothesis of plane-wave propagation. To suppress the incoherent components during the stack of CCFs, the phase-weighted stack (PWS) technique is also included in the proposed workflow. Several synthetic tests have verified the good performance of the new method. Especially when only a few seismic sensors are arranged in the research area, the advantages of our method would be more obvious. Then, the workflow is applied to the analysis of the field noise data, which were collected at Fengman hydropower station, Jilin province, China. The beamforming result indicates that the main component of the signals is produced by the effects of river scouring under the reservoir gate. Finally, the S-wave velocity tomogram of the research area and its geological interpretation are given. All data tests demonstrate that the proposed CWT with PWBB can achieve the stable dispersion measurement from the recorded seismic data of two station.

Plane-wave propagation in media with electromagnetic anisotropy

The propagation of electromagnetic waves in a medium with electrical and magnetic anisotropy is a subject that is not usually handled in conventional optics and electromagnetism books. During this work, we try to give a pedagogical approach to the subject, using tools that are accessible to an average physics student. In this article, we obtain the Fresnel relation in a media with electromagnetic anisotropy, which corresponds to a quartic equation in the refraction index, assuming only that the principal axes of the electric and magnetic tensors coincide. Additionally, we find the geometric location related to the different situations the discriminant of the quartic equation provides. In order to illustrate our findings, we determine the refractive index together with the plane wave equations for certain values of the parameters that meet the established conditions. The target readers of the paper are students pursuing physics at the intermediate undergraduate level.

Dispersion of Love-type wave and its limitation in a nonlocal elastic model of nonhomogeneous layer upon an orthotropic extended medium

This research paper investigates the Love-type surface wave dispersion in a nonlocal elastic nonhomogeneous medium over a nonlocal orthotropic semi-infinite medium under the effect of interior initial stress component. A generalized linear elasticity theory with the nonlocal effect in the fundamental stress-strain relation is adopted to address the equation of motion in layered media. In the case of time-harmonic plane wave propagation, PDEs (cf. equations of motion) of the nonlocal elasticity are reduced to closed-form singular differential equations. The equation of dispersive wave is derived using appropriate plane stress-displacement-continuity conditions of the model. The dispersion of Love-type wave and its limitation in a nonlocal elastic media are analysed graphically using MATLAB software. For the specific model, it is observed that the attenuation of the dispersion of Love-type wave depends on a nonlocal parameter. Also, the dispersive wave becomes nondispersive with zero attenuation for large values (∼0.4) of the nonlocal parameter. In the case of dispersive wave, variation of the phase velocity of the fundamental wave mode for different values of nonlocality, nonhomogeneity, wave number and initial stress parameters are shown graphically. Some special cases are deduced from the original dispersion equation and validated with the published literature.

Propagation characteristics of plane waves in nonlocal isotropic diffusive materials

The size-dependent theoretical modeling of coupled phenomena between deformation and mass diffusion is of current interest in the fields of nanomechanics and nanotechnology. The theory of nonlocal elasticity is applied to study the propagation of plane waves in a linear and isotropic diffusive elastic material. The governing equations of motion are specialized in a plane and are solved for time-harmonic plane wave solutions. The velocity equations are derived to show the possible propagation of three homogeneous plane waves in an isotropic diffusive elastic medium. A reflection phenomenon of plane waves is also considered to obtain the reflection and energy coefficients of reflected waves. A particular numerical example is taken to illustrate graphically the effects of elastic and diffusive nonlocal parameters on the speeds of plane waves, reflection coefficients and energy ratios of reflected waves.

Influence of Diffusion and Impedence Parameters on Wave Propagation in Thermoelastic Medium

The aim of the present paper is to study the impact of diffusion and impedance parameters on the propagation of plane waves in a thermoelastic medium for Green and Lindsay theory (G-L) and the Coupled theory (C-T) of thermoelasticity. Results are demonstrated for impedance boundary conditions and the amplitude ratios of various reflected waves against the angle of incidence are calculated numerically. The characteristics of diffusion, relaxation time and impedence parameter on amplitude ratios have been depicted graphically. Some cases of interest are also derived from the present investigation.

Features of modeling of stress and strain waves in an anisotropic medium on the example of a wooden element

This article describes the hypotheses of the occurrence, propagation, and modification of stress and strain waves caused by external loads in isotropic and anisotropic infinite and finite elastic media. A model of an infinite elastic medium experiencing a point external impulse is presented. The model demonstrates the propagation of a longitudinal plane wave. Compaction and rarefaction of the medium are observed in the plane with wave propagation. A graph of changes in the amplitude of a longitudinal plane wave is presented in the same coordinate system. The problem is posed of expanding the numerical model of a finite elastic medium in the form of an anisotropic wooden rod experiencing a plane external impulse. The model should demonstrate the propagation of longitudinal and transverse waves and describe the volumetric deformation of an anisotropic material. Compaction and rarefaction of the medium are shown in the plane, coinciding with the direction of wave propagation. A graph of the change in the shear wave amplitude is presented in the same coordinate system. The combination of these two graphsreveals the difference in wave propagation velocities and the combination of amplitudes. The model will make it possible to identify the presence of Rayleigh waves and to describe the reflection of waves from the boundary of the medium.