Oblique Incident Waves Research Articles

REALIZATION OF GROUND MOTION INPUT IN ABAQUS FOR LAYERED FOUNDATION UNDER SV WAVE OF OBLIQUE INCIDENCE OVER CRITICAL ANGLE

In the finite element numerical simulation, it is an urgent challenge to determine the ground motion input for the layered foundation under SV wave of oblique incidence over critical angle. Exact dynamic stiffness matrix in the frequency domain (i.e., frequency domain stiffness matrix method) of layered foundation is used to derive the formula for calculating the equivalent node force of ground motion input under arbitrary angular oblique incidence of SV wave, and the validity and accuracy of the ground motion input applied to ABAQUS numerical simulation are demonstrated by simulating seismic wave field of homogeneous half-space and layered foundation under oblique incidence of SV wave through ABAQUS software. It is shown that the inclined SV wave incidence with an arbitrary angle can be realized through ABAQUS simulation by means of stiffness matrix method, and the method is of high accuracy, especially in the case of SV wave incidence with an inclined angle greater than the critical one. The oval like motion trails of surface particles in uniform half space and the wave motion characteristics of layered half space are simulated commendably by finite element numerical modelling. On the above basis, the frequency domain stiffness matrix method is further combined with equivalent linearization method, which solves the ground motion input problem of two-dimensional layered half space considering soil nonlinearity for the inclined incidence with arbitrary angle.

Performance of an U-Shaped Oscillating Water Column Wave Energy Converter Device under Oblique Incident Waves

The present study deals with the performance of an U-shaped oscillating water column device under the action of oblique incident waves. To solve the associated boundary value problem, the dual boundary element method (DBEM) is used. Various physical parameters associated with the U-shaped OWC device, such as the radiation susceptance and conductance coefficients, and the hydrodynamic efficiency, are analyzed for a wide range of wave and structural parameters. The study reveals that the resonance in the efficiency curve occurs for smaller values of wavenumber with an increase in chamber length, submergence depth of the front wall and opening duct, and width of the opening duct. It is observed that with appropriate combinations of the angle of incidence and incident wavenumber, more than 90% efficiency in the U-shaped OWC device can be achieved.

Elastic Metasurfaces for Full Wavefront Control and Low-Frequency Energy Harvesting

Abstract Controlling and manipulating elastic/acoustic waves via artificially structured metamaterials, phononic crystals, and metasurfaces have gained an increasing research interest in the last decades. Unlike others, a metasurface is a single layer in the host medium with an array of subwavelength-scaled patterns introducing an abrupt phase shift in the wave propagation path. In this study, an elastic metasurface composed of an array of slender beam resonators is proposed to control the elastic wavefront of low-frequency flexural waves. The phase gradient based on Snell’s law is achieved by tailoring the thickness of thin beam resonators connecting two elastic host media. Through analytical and numerical models, the phase-modulated metasurfaces are designed and verified to accomplish three dynamic wave functions, namely, deflection, non-paraxial propagation, and focusing. An oblique incident wave is also demonstrated to show the versatility of the proposed design for focusing of wave energy incident from multiple directions. Experimentally measured focusing metasurface has nearly three times wave amplification at the designed focal point which validates the design and theoretical models. Furthermore, the focusing metasurface is exploited for low-frequency energy harvesting and the piezoelectric harvester is improved by almost nine times in terms of the harvested power output as compared to the baseline harvester on the pure plate without metasurface.

Wave RUN-UP Measurements under very oblique wave incidence

Under the scope of the HYDRALAB+ transnational access project, the so-called RODBreak experiment was conducted in the multidirectional wave basin at the Marienwerden facilities of the Leibniz University Hannover (LUH). A stretch of a rubble-mound breakwater was built in the wave basin with a very gentle slope. Its armour layer was made of Antifer cubes, at the roundhead and adjoining trunk, and of rock, at the rest of the trunk. A set of tests was carried out to extend the range of wave steepness values analysed in wave run-up, overtopping and armour layer stability studies, focusing on oblique extreme wave conditions, with incident wave angles from 40º to 90º. The present study focuses on the analysis of measured wave run-up values obtained in the tests and on their on their variability as well as the influence of the wave obliquity and directional spreading. Keywords: rubble-mound breakwaters; run-up; oblique waves; physical modelling; RODbreak.

Active broadband sound transmission loss control through an arbitrary thick smart Piezo-laminated cylinder

The feedback control strategy is utilized for the enhancement of the sound transmission loss (STL) through an infinite thick hollow Piezo-laminated cylinder of arbitrary thickness insonified by an oblique progressive incident plane wave. The close form formulation is accomplished by utilizing the sound wave equation, the three-dimensional (3D) exact theory of elasticity and piezoelasticity. The active control strategy is achieved by sending a control signal from the distributed piezoelectric sensor layer through a controller with certain feedback gain to drive the external piezoelectric actuators. The mechanical stress generated by the piezo-actuator layer cancels the parts of the input incident wave to enhance the STL. Comprehensive numerical studies are carried out to investigate the poling direction and feedback gain effects on the STL. The results show that in the case of radially polarized piezoelectric materials, the feedback control provides significant sound enhancement especially, when the angle of the incident wave is close to normal, however, in the case of axially polarized piezoelectric materials, the control feedback strategy reduces the unfavorable oscillatory motion of the cylinder in addition to providing a superior sound isolation enhancement, particularly for near-grazing incident angles. The accuracy of the proposed solution is confirmed by comparing the presented results with the ones from the simplified models in the literature as well as the commercial finite element package Comsol Multiphysics.

In-situ measurement method of sound transmission loss under an oblique incidence of plane wave

In this study, two-dimensional finite-difference time-domain analysis was used to investigate sound transmission loss (STL) of porous materials with different incident angles. This method has provided evidence for the feasibility of measuring STL in situ using one particle velocity–pressure sensor and one pressure sensor. In the numerical analysis, the total sound pressure and the vertical component of the total particle velocity at the incident side of the material were used to separate incident and reflected components. The STL was calculated using the separated sound pressure at the incident side and the sound pressure at the transmitted side of the porous material. The STL calculated from simulation agrees with theoretical values at all incident angles investigated.

Wideband Microwave Absorber Comprising Metallic Split-Ring Resonators Surrounded With E-Shaped Fractal Metamaterial

A specially designed metallic E-shaped fractal-based perfect metamaterial absorber (PMA) with fairly wideband absorptivity in the K- and Ka-bands of the microwave regime was investigated. The PMA top surface is comprised of square-shaped split-ring resonators (SRRs) surrounded with the stated fractal design. The absorptivity of PMA was analyzed in the range of 20 - 30 GHz for the normal and oblique incidence of waves. Both the transverse electric (TE) and transverse magnetic (TM) modes were taken up to observe the robustness of the proposed design. It was observed that the fractal resonators exhibit capacitive effect at low frequencies, whereas the SRRs manifest capacitive effect at higher frequencies. The simulation and measured results were found to be in fairly good agreement. It is expected that the proposed design of PMA would be useful for 5G communication applications.

Designing Efficient Phase-Gradient Metasurfaces for Near-Field Meta-Steering Systems

We investigate the aptness of various 4 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">th</sup> order (90°) rotationally symmetric phase-transforming cells for the upper phase-gradient metasurface, which always receives an oblique incidence wave from the lower metasurface in a Near-Field Meta-Steering system. A comprehensive study on the behavior of various phase-transforming cells and corresponding supercells when a rotating oblique plane wave impinges on them is presented. First, we select the supercell with high transmission in the desired output Floquet modes, for both TE and TM input modes, when an oblique incidence wave is rotated. The selected supercell is then optimized using Floquet analysis in conjunction with particle swarm optimization (PSO). All the undesired modes are successfully suppressed below -32 dB in the optimized supercell, and the predicted broadside radiation pattern is free of spurious grating lobes. A Near-Field Meta-Steering system with an aperture diameter of 7.3λ <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">0</sub> (110mm @ 20 GHz) is presented. It has a pair of optimized phase-gradient metasurfaces and a dipole antenna array. A maximum peak directivity of 24.2 dB is achieved when the beam is in the broadside direction. The proposed steering system is capable of scanning a conical range with an apex angle of 126° when a 6 dB reduction in peak directivity is allowed. For a 3 dB variation in the peak directivity, the corresponding apex angle is 103°.

Multi-Band Multi-Functional Metasurface-Based Reflective Polarization Converter for Linear and Circular Polarizations

In this paper, we present a simple metasurface based multiband reflective polarization converter for both linear and circular polarizations. We show that, on one hand, the proposed structure can convert the polarization of linearly polarized waves to the orthogonal direction at four frequency bands — 4.3 GHz, 7.2 GHz, 12.3 GHz, and 15.15 GHz. On the other hand, this metasurface can achieve linear to circular or circular to linear polarization conversion at 4 GHz, 4.75–5.95 GHz, 8.35–8.8 GHz and 14.35–14.6 GHz frequency bands. Such multiband operation originates from multiple resonances occurring in the structure based on meandered square ring and diagonal split strip resonator. Moreover, the polarization transforming capability is stable for oblique incident angle up to 15°, for both transverse electric (TE) and transverse-magnetic (TM) polarizations. Furthermore, the proposed structure acts as a meta-reflector that maintains the handedness of the circular polarization upon reflection. Finally, a prototype of the proposed meta-structure is fabricated and measured for both normal and oblique incidence of electromagnetic waves. All the results present excellent resonant stability with respect to the different polarization and incident angles. In addition, we have also performed the tolerance analysis of different material parameters to understand the robustness of the structure. Due to the ability of the structure to perform three functionalities through a single layout, the proposed design can pave its way in different microwave applications such as satellite, radar, and 5G communications.

Asymptotic Representations of the Solution of the Problem on the Wave Field Structure Formed by the Plane Wave Incidence on a Semitransparent Ingomogeneous Plasma Layer (a Model Problem)

Different asymptotic representations of the exact solution of the problem about the oblique incidence of a plane wave on a plasma layer are considered. The plasma layer has a finite thickness and a parabolic profile of the electron density. The large parameter of the asymptotic forms is the ratio of the layer thickness to the wavelength. The following three cases are analyzed: the layer reflecting in the geometrical optics (GO) approximation, the layer being transparent in the GO approximation, and the critical layer. It is shown that the semitransparency effect is significant in the considerable neighborhood of the critical value of the layer parameters for given characteristics of the incident wave. The correct asymptotic forms are suggested for the adequate calculation of this effect. The results of the numerical modeling of the wave field structure are represented in the conditions of the considerable semitransparency effect. These results are compared with the GO solution.

Design of a wideband random phase gradient metasurface by using line-shaped element

Based on phase randomization theory, a method for manufacturing metasurface with diffuse scatter performance is proposed. By using the line-shaped elements with random rotate angles and random distributing positions, the metasurface can achieve good diffusion scatter performance with polarization independent characteristic. This paper studies the effects of the length of line-shaped elements on the metasurface response frequency and the radar cross section (RCS) reduction bandwidth. The simulated result shows that the wideband properties of metasurface benefit from two different length line-shaped elements. The proposed metasurface can reduce the RCS significantly for both normal and oblique incident waves. The line-shaped element is suitable for all sizes of detected objects and it can be directly sprayed on the detected object surface. To demonstrate the effectiveness of the proposed method, the metasurface prototype is fabricated and measured. Experimental results show that the fabricated metasurface can effectively reduce RCS, and it has great application prospects in stealth technology.

Experimentally validated broadband self-collimation of elastic waves

One extraordinary phenomenon exhibited by phononic crystals (PnCs) is that they can manipulate oblique incident waves in a target direction via proper refraction, commonly called wave self-collimation. Although prior studies have demonstrated self-collimation of electromagnetic and acoustic waves, only a few studies have examined elastic waves in this context. If a PnC is designed to represent rectangular-like and/or parallel-line-like equi-frequency contour (EFCs), elastic waves can be self-collimated in either horizontal or vertical directions. However, in the existing literature, there is no theoretical rationale for realizing rectangular-like and/or parallel-line-like EFCs; besides, broadband self-collimation of elastic waves has not yet been explored. Therefore, we propose to derive the material property requirement for an anisotropic PnC to exhibit rectangular-like EFCs (a range of low frequencies) and parallel-line-like EFCs (a range of high frequencies) in the case of elastic waves. Furthermore, by inherently adjoining two frequency ranges of the rectangular-like and parallel-line-like EFCs at a certain frequency, broadband self-collimation covering the entire range of frequencies can be achieved. With the designed anisotropic PnC that fulfills the proposed material property requirement, self-collimation for S0 Lamb waves is numerically simulated and experimentally demonstrated over a broad range of frequencies.

Experimental study of breaker index of normal and oblique incident unidirectional and multidirectional irregular waves on slope

Most studies of wave breaking on slopes to date have investigated regular waves or normal incident unidirectional waves. In this study, wave breakings of normal and oblique incident irregular waves and multidirectional irregular waves on a 1:15 slope were investigated. The breaking criteria of irregular waves based on significant wave height and individual wave height were determined. Firstly, breaker indexes calculated using significant wave heights at incipient breaking were analyzed; they were substantially lower than the breaker indexes of regular waves. The breaker index formulae of irregular waves are presented based on the referred formula of regular waves. Furthermore, the breaker indexes of oblique incident waves were larger than the breaker indexes of normal incident waves. However, wave directionality had little effect on breaker indexes under the present experimental conditions. Secondly, the breaker index (the ratio of significant wave height to water depth) in surf zone was analyzed. It increased with a decrease in relative water depth. Thirdly, information of individual waves in irregular wave trains was tracked by the wave-by-wave method. The breaker indexes derived by individual wave heights were larger than the incipient breaker indexes derived from significant wave heights. Based on previous empirical formulae, some relatively simple expressions are proposed to calculate individual breaking wave heights for unidirectional irregular waves.

Nonperiodic Metasurfaces for Retroreflection of TE/TM and Circularly Polarized Waves

In this article, we propose nonperiodic metasurfaces used for retroreflection of oblique incident wave with linear polarization (TE/TM) and circular polarization (CP). For CP wave, both handedness reversal and handedness preservation cases are demonstrated. The proposed metasurfaces consist of nonperiodic group cells optimized by genetic algorithm for desired scattered power patterns. Each group cell includes several locally periodic elements that are characterized by their reflection phase response under TE/TM or CP illumination. The proposed metasurfaces for retroflection have achieved reduced sidelobe level and suppressed specular beam and are verified by both full wave simulation and measurement at 10 GHz. This nonperiodic metasurface design method offers fast implementation for retroreflection of any plane wave with easy planar fabrication and can be easily scaled to millimeter-wave, THz, and optical regimes.

An exact ray model for oblique incident light on planar films

During recent years, ray tracing has frequently been used to study the absorption characteristics of structured solar cells. However, wave properties such as absorption enhancement due to resonances in optically thin solar films, cannot be explained by pure classical ray models. Here we present an exact three-dimensional ray model for oblique incidence of a plane electromagnetic wave on a thin film and show that the resonant structure of the absorption cross section calculated from our ray model is identical to exact calculations by electromagnetic wave theory. Both parallel and perpendicular polarized light are described exactly by the ray model presented. We validate the resonant structure of the absorption cross section of our ray model by an experimentally realized layered film, where we obtain perfect agreement between experiment and theory. We demonstrate further that for a beam with a finite beam waist, in accordance with Beer-Lambert's law, absorption occurs along the path of the beam, while, in the case of a plane wave incident on an optically thin film, and contrary to Beer-Lambert's law, absorption occurs along the axis perpendicular to the surface of the film. • Presents a three-dimensional ray model that describes exactly the absorption properties of layered materials. • The ray model reveals the resonant structure of the absorption cross section exactly, confirmed by exact wave calculations and experiments. • The paper highlights pitfalls for explaining interference in films by rays, which modern textbooks often are not aware of. • In the case of absorption, the absorption is normal to the surface of the film and not along the path of the classical ray.

Scattering of linear oblique water waves by an elastic bottom undulation in a two-layer fluid

A hydrodynamic model, with incorporation of elasticity, is considered to study oblique incident waves propagating over a small undulation on an elastic bed in a two-layer fluid, with the upper layer exposed to a free surface. Following the Euler–Bernoulli beam equation, the elastic bed is approximated as a thin elastic plate. The surface tension at the interface of the layers is completely ignored since its contribution will be minimal. While considering water waves passing over a deformable bottom, a significant change in the wave characteristics is observed due to the elasticity of the bottom which has an immense impact on the water wave kinematics and dynamics in addition to demonstrating the elastic behavior of the soil beneath. Time-harmonic waves propagate over an elastic bed with two different modes: the one corresponding to the smaller wavenumber propagates along the interface and the other one corresponding to the higher wavenumber along the free surface for any given frequency. Considering an irrotational motion in an incompressible and inviscid fluid, and applying perturbation technique, the first-order corrections to the velocity potentials are evaluated by an appropriate application of Fourier transform and, subsequently, the corresponding reflection and transmission coefficients are computed through integrals containing a shape function which depicts the bottom undulation. To validate the theory developed, one particular undulating bottom topography is taken up as an example in order to evaluate the hydrodynamic coefficients which are represented through graphs to establish the water wave energy conversion between those modes. The observation is that when the oblique wave is incident on the interface, energy transfer takes place to the free surface, but for free-surface oblique incident waves, no such energy transfer to the interface takes place because of the parameter ranges. It is noticed that reasonable changes in the elasticity of the bed have a significant impact when the propagating wave encounters a small elastic bottom undulation. Further, the values of reflection and transmission coefficients obtained for both the interfacial wave mode as well as the free-surface wave mode in the fluid are found to satisfy the important energy balance relations almost accurately. Such problems with a deformable bed, to be precise elastic here, will enable researchers to take up problems which take into account the characteristics of the infinite depth of soil beneath the bed, and the present study is expected to provide the necessary background.

Bistatic scattering at soft–hard strips and plates: method of moments (MoM), theory of edge diffraction (TED), and physical theory of diffraction (PTD) analysis

Diffraction at a strip with one face soft (electric) and the other hard (magnetic) is studied. New results obtained by the method of moments (MoM) are compared with the asymptotic theory of edge diffraction (TED) for the totally soft and hard strips. Attention is given to diffraction of oblique incident waves including the grazing diffraction. Novel analytic estimations for the forward and backward grazing scattering are established via the advanced physical theory of diffraction (PTD) free of grazing singularities. These estimations are demonstrated for the infinitely long strips and finite size rectangular plates.

Analysis, Design, and Implementation of a New Extremely Ultrathin 2-D-Isotropic Flexible Energy Harvester Using Symmetric Patch FSS

Electromagnetic (EM) energy exists far and wide in the environment and can be harnessed and transferred to the desired load(s). The researchers mostly designed and implemented the planar metasurface energy harvester (MEH) offering a restricted look-angle. In this article, we propose an extremely ultrathin 2-D-isotropic flexible MEH using multipolarized patch frequency selective surface. This MEH, which has a curved shape, enjoys a relatively constant performance over a huge range of oblique incident waves. The final structure can be prepared by a small slice of a cylinder. A classic model inspired from the dipole antenna concept is used for impedance matching. Theoretical analyses, design, and fabrication of the structure are presented using a deep subwavelength PCB substrate having a thickness of $\sim 0.004~\lambda _{0}$ . EM energy harvesting is analyzed with an equivalent circuit model. The experimental results are acceptably in agreement with the simulation results. The design can be scaled to different RF bands; however, to provide the required energy for Internet-of-Things (IoT) instruments, we have used WiFi as a crowded frequency band. The simulation efficiency of the flat style extremely ultrathin MEH (EMEH) for normal incidence (at 5.81 GHz) and 60° oblique angle incidence with transverse magnetic (TM) and transverse electric (TE) polarizations are 87.35%, 93.26%, and 64.42%, respectively. In addition, half power bandwidth (HPBW) for these situations is 6.97%, 8.86%, and 5.61%, respectively.

Design and demonstration of a wide-angle and high-efficient planar metasurface lens

In this paper, a gradient index metasurface lens (metalens) for planar wide-angle and high-efficient focusing is designed, fabricated and tested. By properly designing the ultra-thin double-layer metasurfaces with gradient meta-atoms, the proposed metalens can focus wide-angle incident wave efficiently working at transmission regime. The numerical and experimental results demonstrate that the metalens can focus oblique incident wave continuously up to 40°within half maximum focused field intensity of normal one on one side. Besides, the accurate focused spot mapping dependent on both the normal and oblique incident angle is established and analyzed quantitatively. The designed metalens demonstrate good achromatic capability with large spatial incident angle view. This work of wide-angle and high-efficient metalens enhances the performance of conventional ones which operate within narrow incident angle range and can opens up new ways to develop some novel ultra-thin devices like wide-angle scanning antenna and planar retro-reflector in microwave band.

Manipulation of shear horizontal guided wave with arbitrary wave fronts by using metasurfaces

In this work, we proposed a general method to manipulate the fundamental shear horizontal wave (SH0) in plates with arbitrary wave fronts by using metasurfaces consisting of multiple parallel strips. Firstly, the guided waves in infinitely long rectangular strips with different widths were analyzed. The transmission characteristic of the fundamental shear horizontal wave in infinitely long rectangular strips (quasi-SH0) was calculated and the relationship between the phase shift and the frequency-width product is obtained. Secondly, the mode conversion was analyzed for the oblique incidence of SH0 wave from a large plate to a strip, and it was found that the Lamb wave S0 also appeared. Then, the design method for metasurfaces under the incidence of SH0 wave with arbitrary wave fronts was proposed. Two types of metasurfaces, i.e. the flat lenses and the ring-type source illusion devices, were designed to validate the proposed design method. Both simulations and experiments were conducted in which the thickness-shear d15 piezoelectric rings and strips were used as the SH0 wave exciters and the d24 face-shear wafers were used as the wave receiver. Results showed that using the proposed method, different functional metasurfaces can be designed and work well under arbitrary wave fronts incidence. The proposed metasurface design method is potentially useful for practical applications such as nondestructive testing, advanced signal modulation and seismic wave controlling.