Plane Wave Propagation Research Articles

Nonlinear propagation of quasiplanar shear wave beams in soft elastic media with transverse isotropy.

Model equations are developed for shear wave propagation in a soft elastic material that include effects of nonlinearity, diffraction, and transverse isotropy. A theory for plane wave propagation by Cormack [J. Acoust. Soc. Am. 150, 2566 (2021)] is extended to include leading order effects of wavefront curvature by assuming that the motion is quasiplanar, which is consistent with other paraxial model equations in nonlinear acoustics. The material is modeled using a general expansion of the strain energy density to fourth order in strain that comprises thirteen terms defining the elastic moduli. Equations of motion for the transverse displacement components are obtained using Hamilton's principle. The coupled equations of motion describe diffraction, anisotropy of the wave speeds, quadratic and cubic plane wave nonlinearity, and quadratic nonlinearity associated with wavefront curvature. Two illustrative special cases are investigated. Spatially varying shear vertical wave motion in the fiber direction excites a quadratic nonlinear interaction unique to transversely isotropic soft solids that results in axial second harmonic motion with longitudinal polarization. Shear horizontal wave motion in the fiber plane reveals effects of anisotropy on third harmonic generation, such as beam steering and dependence of harmonic generation efficiency on the propagation and fiber directions.

Wave packet enriched finite elements for thermo-electro-elastic wave propagation problems with discontinuous wavefronts

In this article, we study the numerical properties of the recently developed local (element-domain) harmonic basis function enriched finite element (FE) for wave propagation problems. The study includes the effect of the enrichment harmonics on the conditioning of system matrices and how the diagonal scaling mass lumping technique influences the possible ill-conditioning and the solution accuracy. Subsequently, a wave packet enriched thermoelectromechanical FE formulation is presented for axisymmetric and planar wave propagation problems in piezoelastic media. The conventional Lagrange interpolations for the displacement, temperature, and electric potential fields are enriched with the element-domain sinusoidal functions which satisfy the partition of unity condition. The extended Hamilton’s principle and constitutive relations of the Lord–Shulman and Green–Lindsay generalized piezothermoelasticity are employed to derive the coupled system of equations of motion which is solved using Newmark- direct time integration scheme. The performance of the proposed elements is assessed and wave characteristics are studied for the problems of thermoelastic shock waves in an elastic annular disk and thermoelectric shock waves in a piezoelectric hollow cylinder. The element shows significant improvement in the computational efficiency and accuracy over the conventional FE for these problems involving sharp discontinuities in the fields at the wavefronts.

On the propagation of plane waves in cubic quasicrystal plates with surface effects

In this paper, an exact solution of propagation characteristics of plane waves in an infinite cubic quasicrystal plate with surface effects has been derived. Based on the energy density of quasicrystal elastic deformation, the continuum theory of surface elasticity and new boundary conditions for quasicrystal surface layers are derived, from which we obtain an explicit closed form for dispersion relations of quasicrystal plates with the advanced boundary-value problems. The numerical results indicate that the overall stiffness of the quasicrystal plates strengthens with increasing surface elastic parameters and surface residual stresses, resulting in a continuous decrease in the phase velocity.

Extra DoF of Near-Field Holographic MIMO Communications Leveraging Evanescent Waves

In this letter, we consider transceivers with spatially-constrained antenna apertures of rectangular symmetry, and aim to improve of spatial degrees of freedom (DoF) and channel capacity leveraging evanescent waves for information transmission in near-field scenarios based on the Fourier plane-wave series expansion. The treatment is limited to an isotropic scattering environment but can be extended to the non-isotropic case through the linear-system theoretic interpretation of plane-wave propagation. Numerical results show that evanescent waves have the significant potential to provide additional DoF and capacity in the reactive near-field region.

6G Wireless Communications: From Far-Field Beam Steering to Near-Field Beam Focusing

Abstract--6G networks will be required to support higher data rates, improved energy efficiency, lower latency, and more diverse users compared with 5G systems. To meet these requirements, electrically extremely large-scale antenna arrays are envisioned to be key physical-layer technologies. As a consequence, it is expected that some portion of future 6G wireless communications may take place in the radiating near-field (Fresnel) region, in addition to the far-field operation as in current wireless technologies. In this article, we discuss the opportunities and challenges that arise in radiating near-field communications. We begin by discussing the key physical characteristics of near-field communications, where the standard plane-wave propagation assumption no longer holds, and clarifying its implication on the modelling of wireless channels. Then, we elaborate on the ability to leverage spherical wavefronts via beam focusing, highlighting its advantages for 6G systems. We point out several appealing application scenarios which, with proper design, can benefit from near-field operation, including interference mitigation in multiuser communications, accurate localization and focused sensing, as well as wireless power transfer with minimal energy pollution. We conclude by discussing some of the design challenges and research directions that are yet to be explored to fully harness the potential of near-field operation.

Study on the Lateral Dynamic Impedance of Pile Groups in Transversely Isotropic Soil Using Novak’s Plane Model

In order to consider the effect of anisotropy of soil around the pile on the lateral vibration of pile groups, the soil around the pile is regarded as a transversely isotropic medium, and a lateral dynamic interaction model of pile-pile in transversely isotropic soil is established. According to Novak’s plane assumption and wave propagation theory, the lateral vibration of transversely isotropic soil layer is solved by introducing potential function and using mathematical and physical means, and the attenuation function of lateral displacement of free field is given. The Dobry and Dazetas simplified solution of attenuation function is different from that of solution of plane model. The pile-pile horizontal dynamic interaction factor in transversely isotropic soil is obtained by using the initial parameter method and Krylov function. The horizontal dynamic impedance of pile groups is obtained by using the pile-pile superposition principle. The change rule of the lateral displacement attenuation function of transversely isotropic soil with frequency is related to the direction and frequency. The ratio G h v of the shear modulus in the lateral plane to the shear modulus in the vertical plane and the pile spacing S / d have a great impact on the lateral vibration of pile groups, and when the pile spacing is large, the curves of attenuation function varying with frequency fluctuate greatly. The ratio of elastic modulus of pile to vertical plane shear modulus of soil E p / G v has an effect on the lateral stiffness of pile groups, which is related to frequency, while the effect on dynamic damping is not affected by frequency. The difference of mechanical properties on different surfaces of soil around the pile has a great influence on the lateral vibration of pile groups in transversely isotropic soil, and the influence of the anisotropy on the attenuation function of the lateral displacement and the dynamic impedance cannot be ignored.

Shape and non-shape unified isogeometric optimal design for extremal band gaps

A unified shape and non-shape design optimization for lattice structures is performed to obtain extremal band gaps in an isogeometric computational framework, which uses the same NURBS basis functions as used in CAD description. Using a precise numerical model in both response and shape sensitivity analyses, enhanced response and sensitivity can be obtained, which leads to a precise optimal design. A plane wave propagation in infinite periodic lattice is analyzed within a representative unit cell using the Bloch theory with periodic boundary conditions. The ligaments of lattice structures are modeled using geometrically exact beams whose cross-sectional area and configuration are regarded as design variables, which are parameterized by the NURBS basis functions. The design variables are controlled by a mathematical programming algorithm with efficient adjoint design sensitivity. The obtained optimal lattice structures of triangular, squared, hexagonal, and Kagomé structures are fabricated using a 3D printing machine to be validated by physical experiments. Through harmonic response analysis and physical experiment for the optimal and the original designs, the wave attenuation properties are compared to demonstrate the validity of the obtained optimal design.

Optimization of vibration characteristics and directional propagation of plane waves in branching ligament structures of wind models

To achieve multi-frequency vibration suppression and wave propagation modulation, eight branching ligament structures for wind models are proposed. Using lattice theory, dynamical model and finite element release method, the structures are verified to have multi-frequency bandgaps. By attaching a solid disc at the center of the model, the bandgap coverage of the structure is improved and the bandgap frequency is reduced. The modal analysis shows that the vibration of branch ligaments and border ligaments has a suppression effect on elastic waves. The phase constant surface, phase velocity and wave propagation direction plots at specific frequencies are calculated to verify the directional and regional nature of wave propagation. And the good correspondence of group velocity and wave propagation finite element simulation results at specific frequencies. Finally, the calculated bandgap frequency range is compared with the vibration transfer function, and the two agree well. And the stress cloud diagram also shows that the optimized structure has an excellent vibration suppression capability. The innovatively designed structure has the combined advantages of light weight, ease of fabrication, wide frequency and low frequency vibration control, while the integrated in-plane wave analysis provides the theoretical basis for structural optimization.

Morphological and acoustic modeling of the vocal tract

In speech production, the anatomical morphology forms the substrate on which the speakers build their articulatory strategy to reach specific articulatory-acoustic goals. The aim of this study is to characterize morphological inter-speaker variability by building a shape model of the full vocal tract including hard and soft structures. Static magnetic resonance imaging data from 41 speakers articulating altogether 1947 phonemes were considered, and the midsagittal articulator contours were manually outlined. A phoneme-independent average-articulation representative of morphology was calculated as the speaker mean articulation. A principal component analysis-driven shape model was derived from average-articulations, leading to five morphological components, which explained 87% of the variance. Almost three-quarters of the variance was related to independent variations of the horizontal oral and vertical pharyngeal lengths, the latter capturing male-female differences. The three additional components captured shape variations related to head tilt and palate shape. Plane wave propagation acoustic simulations were run to characterize morphological components. A lengthening of 1 cm of the vocal tract in the vertical or horizontal directions led to a decrease in formant values of 7%-8%. Further analyses are required to analyze three-dimensional variability and to understand the morphological-acoustic relationships per phoneme. Average-articulations and model code are publicly available (https://github.com/tonioser/VTMorphologicalModel).

A Wideband Generalization of the Near-Field Region for Extremely Large Phased-Arrays

The narrowband and far-field assumption in conventional wireless system design leads to a mismatch with the optimal beamforming required for wideband and near-field systems. This discrepancy is exacerbated for larger apertures and bandwidths. To characterize the behavior of near-field and wideband systems, we derive the beamforming gain expression achieved by a frequency-flat phased array designed for plane-wave propagation. To determine the far-field to near-field boundary for a wideband system, we propose a frequency-selective distance metric. The proposed far-field threshold increases for frequencies away from the center frequency. The analysis results in a fundamental upper bound on the product of the array aperture and the system bandwidth. We present numerical results to illustrate how the gain threshold affects the maximum usable bandwidth for the n260 and n261 5G NR bands.

Propagation of plane waves in a nonlocal transversely isotropic thermoelastic medium with voids and rotation

AbstractThe objective of present research work is to investigate the propagation of time harmonic plane waves in a rotating, nonlocal, transversely isotropic thermoelastic half‐space having void pores in the context of Lord–Shulman theory. It has been observed that four coupled plane waves travel in such type of medium with distinct speeds. Using appropriate boundary conditions, the amplitude and energy ratios for the reflected waves are presented. Numerical computations for a magnesium crystal‐like material are performed with the help of MATLAB software to study the effects of material anisotropy, nonlocal, void and rotation parameters on the amplitude ratios. The computational results are displayed and explained through graphs. The phase velocities of plane waves in transversely isotropic medium are found to depend upon the incident angle, whereas these attain constant values in an isotropic medium. The energy conservation law is also justified during the reflection phenomena.

Loss-gain compensated anti-Hermitian magnetodielectric medium to realize Tellegen nihility effects.

Generalized duality transformations significantly modify the constitutive relations of electromagnetic media, preserving principal electromagnetic properties. Here, we contemplate transformation of Tellegen nihility as a specific type of extreme-property nonreciprocal bi-isotropic media and show that some intriguing electromagnetic properties of that medium can be realized in a particular class of isotropic magnetodielectric media without magnetoelectric coupling. We show that the permittivity and permeability of the corresponding transformed medium have equal absolute values and opposite signs. Depending on the value of the Tellegen parameter of the original medium, the transformed magnetodielectric medium can be Hermitian, non-Hermitian, or anti-Hermitian, which simultaneously exhibits loss and gain. Focusing on the latter class of anti-Hermitian media, we theoretically and numerically demonstrate that this extraordinary medium allows propagation of electromagnetic plane waves having zero time-averaged Poynting vector, similarly to the original Tellegen nihility media. Hopefully, this work can open novel opportunities for manipulating electromagnetic fields.

Reproduction of acoustic evanescent waves using wave field synthesis by controlling phase differences between monopole secondary sources

This paper is about the reproduction of acoustic evanescent waves using the linear distribution of discrete monopole secondary sources. The driving function for the actuation of a secondary source is derived using the theory of wave field synthesis. The analysis of the synthesized wave field is done for different source excitation frequencies. A new method of creating more precise evanescent waves based on the phase difference between the sources is also presented. The simulation result shows that the driving function obtained using the WFS method results in the correct synthesis of evanescent wave below aliasing frequency. Above the aliasing frequency, when the consecutive secondary sources are in antiphase, it will produce evanescent waves. Otherwise, propagating plane waves get produced. Different errors in the reproduced wave field which comes due to the use of discrete and fixed array length are also investigated, and some solutions to mitigate those errors are presented.

Plane waves in Moore–Gibson–Thompson thermoelasticity considering nonlocal elasticity effect

The Moore–Gibson–Thompson (MGT) generalized thermoelasticity theory together with the Eringen’s nonlocal elasticity model is used to study the propagation of harmonic plane waves in an infinite elastic medium that conducts heat. Two sets of coupled longitudinal thermoelastic waves have been initiated. These waves are dispersive in nature and experience attenuation. In conjunction with the coupled waves, there also exists one uncoupled vertically shear–type (SV-type) wave. The SV-type wave is dispersive in nature but without any attenuation. The elastic nonlocality parameter influences all these waves. Furthermore, the SV-type wave faces critical frequency, while the coupled longitudinal waves may face critical frequencies conditionally. We also explore the problem of reflection of thermoelastic waves at a stress-free insulated and isothermal plane boundary of the medium considered here. The reflection coefficients and their respective energy ratios of the reflected waves to that of incident wave are determined analytically and numerically by considering an appropriate material. The numerical results are presented graphically to highlight the effects of various parameters of interest. Some important observations about the prediction of the MGT model in comparison to the other existing models (Lord–Shulman (LS) and the Green–Nagdhi theory of type III (GN-III) models) are highlighted.

The problem of propagation of a one-dimensional plastic wave in the environment with linear and polyline unloading

Problems of propagation of plane and spherical waves in a nonlinearly compressible medium with linear and broken line unloading under intense loads are considered. The solutions of the problems are constructed in the opposite way, assuming that the medium at the shock wave front is instantly loaded in a nonlinear manner, and behind the front in the perturbed region, the medium is irreversibly unloaded. For a specific structure of the medium, the results of calculations are presented in the form of graphs of pressure, velocity of the medium at the layer boundary, at the shock wave front and in the disturbed region as a function of time. The influence of the nonlinear properties of the medium on the distribution of the dynamic characteristics of shock-wave processes in it has been studied.

Plane-Wave Generation through General Near-Field In-Band Reflectarray Direct Layout Optimization with Figure of Merit Constraints in mm-Wave Band

A general near-field (NF) in-band synthesis strategy is presented for the direct layout optimization (DLO) of reflectarrays with application to the generation of plane waves for the mm-wave band. The technique relies on the definition of relevant figures of merit (FoM) and the use of a gradient-based minimization algorithm. To this end, the volume where the NF is computed is divided into a number of disjoint regions where the FoM are defined. These FoM define the performance of the antenna and their direct optimization enables improvement compared to previous approaches described in the literature, while reducing the memory footprint of the algorithm and accelerating computation. The optimization procedure is divided into several stages to facilitate convergence towards a successful outcome. First, a phase-only synthesis is carried out at a single frequency. Then, a reflectarray layout is obtained using a method of moments based on local periodicity, accounting for mutual coupling between elements. Finally, an in-band DLO is performed at a number of frequencies directly optimizing the FoM. The results show that the obtained reflectarray layout complies with the requirements in the frequency range 27 GHz–29 GHz within the 5G new radio n257 band.

Plane wave propagation and fundamental solution in functionally graded couple stress micropolar thermoelastic solid with diffusion and voids

In the present problem, we study plane wave propagation and establish fundamental solution in the theory of functionally graded couple stress micropolar thermoelastic solid with diffusion and voids. We observe that there exists a set of four coupled waves namely plane wave(P), thermal wave(T), mass diffusion wave(MD), rotational wave(R) and a set of two coupled waves namely transverse waves(SV1 and SV2) with different phase velocities. The effect of couple stress and voids on phase velocity, attenuation coefficient, penetration depth and specific loss has been studied numerically and presented graphically with respect to angular frequency. It has been observed that characteristics of all the waves are influenced by couple stress and void parameter. Fundamental solution of differential equations of motion in case of steady oscillations has been constructed by using vector calculus and various numerical approaches. Deductions has been made from the present work and compared with the existing result. The analysis of fundamental solution is very helpful to investigate the various problems of functionally graded couple stress micropolar thermoelastic solid with diffusion and voids. The graphical analysis of present study is also very beneficial in order to study the different fields of geophysics, electronics and aerospace like seismology, volcanology, telecommunication, manufacturing of aircrafts etc.

An implicit FFT-based method for wave propagation in elastic heterogeneous media

An FFT-based algorithm is developed to simulate the propagation of elastic waves in heterogeneous d-dimensional rectangular shape domains. The method allows one to prescribe the displacement as a function of time in a subregion of the domain, emulating the application of Dirichlet boundary conditions on an outer face. Time discretization is performed using an unconditionally stable beta-Newmark approach. The implicit problem for obtaining the displacement at each time step is solved by transforming the equilibrium equations into Fourier space and solving the corresponding linear system with a preconditioned Krylov solver. The resulting method is validated against analytical solutions and compared with implicit and explicit finite element simulations and with an explicit FFT approach. The accuracy of the method is similar to or better than that of finite elements, and the numerical performance is clearly superior, allowing the use of much larger models. To illustrate the capabilities of the method, some numerical examples are presented, including the propagation of planar, circular, and spherical waves and the simulation of the propagation of a pulse in a polycrystalline medium.

Investigating wave transmission and reflection phenomena in pantographic lattices using a second-gradient continuum model

In this study, linear plane wave propagation in pantographic lattices is investigated using a two-dimensional (2D) second-gradient continuum model. Primarily, we aim to investigate wave transmission and reflection phenomena occurring when a pantographic lattice is attached to a material modeled by classical first-gradient theory. From a practical point of view, this would be a possible application for pantographic lattices due to their promising mechanical behavior. From a theoretical point of view, this investigation let us to elucidate wave propagation between second- and first-gradient continua. The adapted second-gradient model is first linearized, and the dispersion relations are obtained. Boundary and jump conditions at the discontinuity surface are identified accordingly. It is shown how elastic constants may affect the wave propagation between the two continua and can be tuned to control such wave propagation phenomena.

Generalized Plane Waves in a Rotating Thermoelastic Double Porous Solid

The propagation of plane waves in a rotating homogeneous, isotropic, thermoelastic solid with double porosity following Lord-Shulman’s theory of thermoelasticity has been investigated. It is assumed that the medium rotates about an axis normal to the surface with a uniform angular velocity. There may exist five coupled waves that evolved due to the longitudinal, transverse disturbance, voids of type-I and type-II, and temperature change in the medium. The secular equation for the model under consideration has been derived with the help of formal solutions and boundary conditions. The amplitude of displacements, temperature change and volume fraction fields for voids of type-I and type-II have also been computed analytically. Finally, numerical computations have been carried out for magnesium crystal material to understand the behavior of amplitude of phase velocity, penetration depth, specific loss, displacement components, temperature change, and volume fraction field due to type-I and type-II voids corresponding to the different rotation rates. Various graphs have been plotted to support the analytical findings. The study may be used in the development of rotation sensors, material design and thermal efficiency.