Oblique Incident Waves Research Articles

Nonlinear Seismic Response of Tunnel Structures under Traveling Wave Excitation

Tunnels traditionally regarded as resilient to seismic events have recently garnered significant attention from engineers owing to a rise in incidents of seismic damage. In this paper, the reflection characteristics of the elastic plane wave incident on the free surface are analyzed, and the matrix analysis method SWIM (Seismic Wave Input Method) for the calculation of equivalent nodal loads with artificial truncated boundary conditions for seismic wave oblique incidence is established by using coordinate transformation technology, according to the displacement velocity and stress characteristics of a plane wave. The results show that the oblique incidence method is more effective in reflecting the traveling wave effect, and the “rotational effect” induced by oblique incidence must be considered for P wave and SV wave incidence, including the associated stress and deformation. This effect exhibits markedly distinct rotational phenomenon. In particular, the P wave incidence should be focused on the vault and the inverted arch due to the expansion wave. With the increase of the oblique incidence angle, the structural stress and deformation are rotated to a certain extent, and the values are significantly increased. Simultaneously, the shear action of the SV wave may result in “ovaling” of the tunnel structure, thereby facilitating damage to the arch shoulder and the sidewall components. As the oblique incidence angle, the potentially damaging effects of the “rotational effect” to the vault and the inverted arch, but the numerical value does not change significantly. In addition, in comparison to a circular cross-section, the low-frequency amplification of seismic waves in the surrounding rock and the difference of frequency response function in different parts of the lining are more pronounced. In particular, the dominant frequency characteristics are significant at P wave incidence and the seismic wave signal attenuation tends to be obvious with increasing incidence angle. In contrast, SV waves exhibit more uniform characteristics.

Modeling obliquely incident seismic wave propagation in rocks via the FDM-DEM coupling scheme: Algorithms and applications

The incidence angle of seismic waves plays a pivotal role in the stability analysis of structures in near-field zones. Despite its importance, the application of obliquely incident seismic waves within models of discontinuous media has been limited. This study introduces a novel approach that integrates the oblique incidence of seismic waves into a coupled model employing both the Finite Difference Method (FDM) and the Discrete Element Method (DEM). We validate the accuracy of seismic wave propagation under oblique incidence in two FDM-DEM coupling models—overlapping coupling and interface coupling—through comparisons with theoretical solutions. For vertically incident seismic P-waves, both models yield similar results. However, under oblique incidence, the overlapping coupling model demonstrates superior accuracy, with a maximum error of approximately 4.217 %, compared to about 10 % in the interface coupling model. Our findings also show that while the relative sizes of particle diameter and overlap length minimally affect accuracy, the arrangement of particles markedly influences the results. Furthermore, we apply this method to a slope model to investigate the failure process, revealing that the nature of the sliding body shifts from tensile sliding to tensile ejection as the incidence angle increases.

Ultra-Thin Metasurface Polarization Converter with Linear and Circular Polarization Features for RCS Applications

AbstractIn this study, an attractive ultra-thin metasurface (MS) converter is proposed for both K-band (18–27 GHz) and Ka-band (27–40 GHz) having the superior performance of the linear-to-linear polarization (LP-LP) conversion and the linear-to-circular polarization (LP-CP) conversion. Its operating bandwidth for the LP-LP conversion is approximately over 18.6–26.7 GHz (lower part of the K-band) with a conversion efficiency of more than 90% and over 19.55–24.8 GHz (upper part of the K-band) with a polarization conversion ratio (PCR) value of more than 99%. In addition, its operating bandwidth for the LP-CP conversion (a left-handed circular polarization (LHCP)) is nearly between 31.8 and 40.5 GHz (Ka-band) with a PCR value of more than 99%. The converter can achieve a PCR value greater than 90% for both the LP-LP and LP-CP conversions for an oblique incidence wave with an incidence angle up to $$ 40^\circ $$ 40 ∘ . The design also provides mono-static radar cross section for the 18.6–26.7 GHz frequency range, where the LP-LP conversion is provided. The proposed structure can be considered to be ultra-thin having a thickness of 1 mm corresponding to 0.075$$\lambda $$ λ in the LP-LP and 0.12$$\lambda $$ λ in the LP-CP cases concerning the center frequency. The cost-effective bandwidths (BWCEs) are 210 and 34 for the LP-LP and LP-CP conversions, respectively. Free-space experiments were carried out at X-band and Ku-band to validate our design.

Frequency shifting of plasmon polariton defect modes in a non-Hermitian finite heterostructure

A finite photonic layered system alternating usual media with a dispersive metamaterial with two central layers in a PT- symmetric arrangement is investigated under the oblique incidence of an electromagnetic wave. We have found a defect mode within the gap, and we have studied its optical properties under the influence of gain and loss distributed in these central layers. As a consequence of PT-symmetry in the system, we find that exceptional points can be attracted to or repelled from each other depending on which side of the frequency band under study. Below the plasmon frequency, repulsion occurs between pairs of exceptional points, while above it they attract each other.

Effect of Fixed Bended Plate on Obliquely Incident Waves in Deep Water

Effect of Fixed Bended Plate on Obliquely Incident Waves in Deep Water

Programmable metasurfaces with high angular stability for arbitrarily-polarized obliquely-incident waves

Programmable metasurfaces show enormous potential in real-time electromagnetic (EM) manipulation and their stable responses to variable EM waves including incident angle and polarization changes are crucial for related applications. However, the demonstrated programmable metasurfaces are commonly considered in normal-incident waves with fixed polarization; how to achieve stable performance in more realistic scenarios of wide-angle and full-polarized wave incidences is still a challenge. Here, we propose and realize a wide-angle and full-polarization programmable metasurface, which can generate stabilized amplitude and phase responses at both transverse electric (TE) and transverse magnetic (TM) oblique incidences. These are achieved by introducing metallic walls around the metasurface element to reduce element coupling, which greatly improves the angular stability of its reflection responses. The mechanisms of angular insensitivity are analyzed comprehensively, and as a proof of concept, obliquely-incident beam steering, large-angle beam scanning and oblique vortex beam emitting are demonstrated on this programmable metasurface. Both the simulation and experimental results demonstrate that the programmable metasurface can operate well at both TE and TM wide-angle oblique incidences in the upper half space. Our work offers an actual route for improving the angular stability and polarization insensitivity of metasurfaces, which could push them one step closer towards more complicated applications.

Inversion study of dam incidence angle under oblique incidence of seismic waves

Determination of seismic wave incidence angle is a critical step in performing seismic oblique incidence analysis of dams. However, for structures with complex dynamic responses, such as dams, it is difficult to derive the incident angle by traditional mathematical methods. For this reason, this paper proposes a method for determining the seismic wave incidence angle based on the dynamic response of the dam. The model calculates the dynamic response of the dam under different incidence angles of seismic waves, establishes the mapping relationship between the dynamic response and the incidence angle by using a hybrid particle network, and performs feature screening to obtain the optimal inversion features by the SHAP method, and then constructs the optimal inversion model. The results show that there is a significant correlation between the dynamic response of the dam body and the incident angle, the correlation coefficients of the model are all greater than 0.96, and the average absolute percentage errors are less than 5 %, which proves that the model can effectively invert the incident angle. The method can also be applied to the seismic safety analysis of other structures, providing a new way to determine the seismic wave incidence angle.

Study of the dynamic interactions between helix-stiffened cement mixing piles and soft soil under oblique incidence of SV waves in arbitrary space

Helix stiffened cement mixing (HSCM) piles are extensively utilized in soft soil sites due to their excellent seismic and pullout resistance. Initially, the equivalent nodal force formulas for each face under the oblique incidence of SV waves in any spatial direction are derived based on the viscous-spring artificial boundary. The method's applicability in studying pile–soil interactions is verified based on existing pile–soil tests. Subsequently, the HSCM pile–soil model is constructed using finite element software through a Python program. Various analyses of accelerations, relative displacements, soil reactions, and pile–soil dynamic p-y curves are conducted using two different directions of incidence angles (horizontal and vertical) and various types of seismic waves. Subsequently, the backbone line of the dynamic p-y curve is plotted, revealing the pile–soil interaction mechanism under spatial oblique incidence. Finally, Matlock's formula is modified to ensure its applicability to pile–soil interactions under spatially oblique incidence. The results demonstrate that loading the Kobe wave causes the peak acceleration in the x direction, the peak pile–soil relative displacement, and the peak pile-side soil reaction force to increase by 22.64 %, −18.90 % and 18.42 %, respectively, compared to those of the El Centro wave.

Numerical study on ultrasonic detection of cracks in metallic structures with variable cross-sectional thickness

The metal structures are widely used in aerospace engineering, especially in joints and spars. The safety of these parts is important to ensure the safe service of the whole structures. The ultrasonic wave is a traditional technique to detect cracks in metals. However, it is usually difficult to find all the cracks because of its difficulty in variable directions of the crack and the irregular shapes of the metals. This paper aims to address the challenge of detecting cracks in metallic structures with varying cross-sectional thicknesses using ultrasonic methods. The research investigates the behavior of ultrasonic longitudinal and transverse waves as they propagate through aluminum plates with variable cross sections. Additionally, it examines how cracks in different orientations influence these wave types. The theoretical analyses are performed which explore the reflection of oblique incidence waves and the diffraction of ultrasonic waves when they encounter semi-infinite cracks. Subsequently, numerical simulations are performed to validate the theoretical findings and to detect both horizontal and vertical cracks within metal plates of varying cross-sectional thicknesses. The findings indicate that both longitudinal and transverse waves are effective in identifying the location of damage caused by horizontal cracks. However, when it comes to vertical cracks, only transverse waves are successful in detecting their precise location. From the research of this paper, transverse ultrasonic wave is suggested to detect cracks in metal structures with irregular cross sections.

Spinning spoof surface plasmons and their topological responses

Spoof surface plasmons (SSPs) mimic characteristics of optical surface plasmons in microwave and terahertz frequencies. Manipulating SSPs has attracted widespread attention for extending plasmon applications into the low-frequency range. In this Letter, we show that spinning SSPs can be excited on a twisted groove (TG) metallic cylinder by oblique incident waves. The incident angle of waves and the twist angle of the grooves play essential roles in manipulating the propagation orientation and the rotation direction of spinning SSPs (SSSPs). Finally, we discuss an application of the SSSPs in topological photonic systems. By periodically arranging the TG cylinders, we show that this spinning feature will lead to topologically non-trivial bands in such a photonic crystal, where the topologically protected edge modes arise near the boundary.

Material extrusion 3D printing of large-scale SiC honeycomb metastructure for ultra-broadband and high temperature electromagnetic wave absorption

Electromagnetic (EM) wave absorbing materials have been widely used in various equipment to reduce the interference caused by EM waves. However, current EM wave absorbing materials are limited by narrow absorption bandwidth under high temperatures due to a lack of structural design. Herein, SiC ceramic and large-scale SiC honeycomb metastructure were monolithically fabricated by material extrusion 3D printing. The real permittivity and imaginary permittivity of as-obtained SiC ceramic approached 10 and 2.3 within the frequency of 2–18 GHz. After optimized structure design, the as-obtained SiC honeycomb metastructure exhibited broadband EM performance of −10 dB effective bandwidth from 4.85 to 39.49 GHz (34.64 GHz) when the incident angle was 60° at room temperature. Moreover, the as-obtained SiC honeycomb structure had a stable broadband −10 dB effective bandwidth of above 35 GHz when the incident angle is 60° even after in-situ 1000 °C and ex-situ 1600 °C erosion in the air atmosphere. Broadband EM wave absorption under oblique incident wave was also achieved from 30° to 60° both in transverse electric (TE) polarization and transverse magnetic (TM) polarization. This novel strategy unravels the potential of additive manufacturing of high-performance EM wave absorbers for high temperature environment applications.

Application of Regularized Meshless Method with Error Estimation Technique for Water–Wave Scattering by Multiple Cylinders

In this manuscript, we will apply the regularized meshless method, coupled with an error estimation technique, to tackle the challenge of modeling oblique incident waves interacting with multiple cylinders. Given the impracticality of obtaining an exact solution in many real engineering problems, we introduce an error estimation technique designed to achieve reliable solutions. This technique excels in providing dependable solutions that closely approximate analytical solutions. An additional advantage is its capacity to identify the optimal number of points for both source and collocating points, thereby enhancing computational efficiency. The validity of the proposed method will be demonstrated through three numerical cases, presenting results that exhibit substantial agreement.

Dynamic Response and Failure Analysis of Underground Openings to Oblique Wave Incidence

Dynamic Response and Failure Analysis of Underground Openings to Oblique Wave Incidence

Terahertz Polarization-Resolved Spectra of the Metamaterial Formed by Optimally Shaped Omega Elements on a Silicon Substrate at Oblique Incidence of Waves

The reflection and transmission spectra of a metamaterial formed by omega-shaped elements with pre-calculated optimal parameters on a silicon substrate have been recorded in the terahertz range at oblique incidence for the s- and p-polarizations of the incident wave. The spectra were interpreted within the dipole radiation theory of electromagnetic waves. Both measurement results and analysis provide evidence supporting the presence of a pronounced polarization anisotropy impact in the reflection and transmission of the metamaterial. The potential of these materials to be utilized in the development of devices that control the polarization properties of THz radiation across a wide spectral range is examined.

Oblique wave trapping by sinusoidal rippled barrier of finite thickness placed on closely spaced semi-circular seabed

The oblique wave trapping by a sinusoidal rippled barrier (SRB) of finite thickness placed far away from a partially reflecting seawall is examined under the assumption of linear potential flow theory. The sinusoidal ripples are identical, and the barrier is installed in the presence of a semi-circular bottom (SCB). As a special case, the wave trapping by a thick non-rippled barrier (NRB) is also studied to show the significance of the ripples on the wave trapping. The multi-domain boundary element method is employed to tackle the wave-trapping performance of the SRB satisfying Darcy's law. Various types of structural configurations, such as (a) SRB alone, (b) SRB placed on SCB with trapping chamber, (c) without trapping chamber, (d) NRB alone, and (e) NRB placed on SCB with trapping chamber, are proposed and evaluated under oblique wave incidence. The correctness of the study results is verified with the available results for specific structural configurations. The effect of wall reflection, chamber length, plate porosity, and plate submergence depth on wave-trapping coefficients (wave reflection and wave run-up) and force coefficients (horizontal force on the wall and vertical force on the barrier) are presented against relative wavelength. The enhanced wave trapping is obtained after installing a SRB when compared with the NRB of finite thickness. The chamber spacing minimizes the trapping coefficients when compared with the non-chamber rippled barrier. The study recommends the SRB with SCB of thickness 0.10≤D/h≤0.15, porosity 20%, width B/h=2, and chamber spacing 1≤L/h≤2 to replace the gravity-type breakwaters to be installed against intermediate and deep-water waves.

A simulation approach for site-city interaction in basin under oblique incident waves and its applications

The coexistence of basin effects and site-city interaction (SCI) effects will result in a more complex spatially differentiated distribution of seismic wavefields and building responses. However, current research still lacks investigation into the SCI effect under three-dimensional (3D) oblique incidence in basins. This paper employs the Spectral Element Method (SEM) to simulate the propagation of seismic wavefields in near-surface soil, utilizes a nonlinear Multi-Degree-of-Freedom (MDOF) model to simulate buildings, and combines the Frequency-Wavenumber (FK) domain method to input oblique incident seismic wavefields as equivalent seismic loads, thereby establishing the FK-SE-MDOF approach. This approach addresses the limitation of neglecting the influence of oblique incidence when studying the impact of SCI in basins, and has been developed into SPECFEM 3D. First, the theory of the FK-SE-MDOF approach was introduced, and the correctness of this approach was validated. Furthermore, taking a series of SCI model in an ideal basin as an example, calculations and analyses were conducted to investigate the effects of factors such as the relative layout of the basin and building cluster, incidence angles, and basin stratigraphy on site seismic wavefields and building responses. This approach can provide a quantitative reference for seismic design, risk assessment, and post-earthquake rescue efforts.

Dynamic responses of a bituminous concrete core rockfill dam on layered overburden under seismic wave input

The dynamic nonlinearity, overburden stratification characteristics and oblique incidence of seismic waves in soil greatly increase the difficulty of determining the free field of a dam foundation, which restricts seismic input accuracy. Based on the potential function theory, this paper constructs a transfer relationship between the wave amplitude matrix at the top layer of a dam foundation with overburden and the wave amplitude matrix at any layer and obtains the shear strain of the soil through Fourier inverse transformation. Then, the equivalent linearization method is adopted to depict the nonlinearity of the soil. An analytical calculation method for the free field of a dam foundation with layered overburden under inclined seismic waves is proposed. This method can not only forward the free field according to the incident wave in the deep part of the foundation but also directly invert the free field according to the seismic motion on the ground surface, and the inversion efficiency is high. Using a nonlinear viscous-spring boundary element developed by the authors, combined with the free field, a wave input method for a dam foundation with a layered overburden under inclined seismic waves is established. The maximum error between the numerical solution under wave input and the analytical solution is only 5%. The computational precision of the method is high. Finally, the dynamic responses of a bituminous concrete core rockfill dam on a layered overburden are studied. The results show that an upstream buoyancy and oblique incidence are the main reasons for a larger acceleration on the upstream side of the dam than on the downstream side. As the incident angle increases, the differential distribution becomes more significant, and the amplification coefficient of the anti-seepage system also increases. When the incident angle is 25°, the horizontal and vertical amplification coefficients at the top of the core wall increase by 12.8% and 25.2% compared to the vertical incidence, respectively. The accelerations of the dam are overestimated under uniform seismic input, and the amplification coefficients of the dam crest are overestimated by 52.3% and 39.8% compared with the wave input, respectively. The wave input reasonably solves the problem of seismic input for a dam foundation with layered overburden, considers the inclined seismic waves, and can reflect the seismic waves propagation characteristics. The wave method provides a solid foundation for the seismic safety of rockfill dams with layered overburden.

Frequency‐independent Sound Absorbing Metamaterials

AbstractInspired by the concept of frequency‐independent antennas in the electromagnetics, which theoretically exhibit a frequency‐independent bandwidth, this paper extends the concept to acoustics by adopting a log‐spiral and its modified shape to introduce a class of metamaterials called frequency‐independent sound‐absorbing metamaterials. Without the requirement of multiple resonators, these metamaterials achieve an ultra‐broadband absorption spanning from 550 Hz for a wide range of incident angles up to 80°, using a single unit cell structure owing to Fabry–Pérot resonance, viscous boundary losses, and thermoviscous loss of the foam. Numerical and experimental analyses are provided to demonstrate the working principles of the proposed structures. Their performance is compared with archimedean spiral, and the influence of air and porous material parameters on the performance of the metamaterial is discussed in detail for normal and oblique incident waves. The underlying principle is discussed in detail, highlighting the distinctions between the proposed structures and state‐of‐the‐art broadband metamaterials. The proposed structures represent a pioneering advancement in the field by offering compact and ultra‐broadband sound‐absorbing metamaterials that are suitable for practical applications.

Multipole solution with nonlinear pressure loss for oblique waves action on a submerged partially perforated semi-circular breakwater

This study is an extension of the research on semi-circular breakwater based on Lyu et al. (2020). This time, we focus on the changes in the flow field when waves obliquely interact with the axis of the partially perforated semi-circular breakwater, as well as the nonlinear effects resulting from variations in wave height to some extent. The analytical solution of the flow field is still obtained using the multipole expansion method based on potential flow theory and the method of separation of variables. The analytical solution for oblique incidence is primarily achieved through the cylindrical form of the Bessel equation. Separately considering viscous effects and potential flow, we estimate the impact of wave height variation on the perforated boundary through the quadratic pressure loss term. By employing an iterative solving approach, we comprehensively discuss the influence of wave height, water depth, perforation form, and oblique incidence angle on the flow field and the forces acting on the breakwater.

Light absorption by a planar array of spherical particles and a matrix in which they are embedded: statistical approach.

The fractions of light energy absorbed by a 2D array of spherical particles and the matrix in which they are embedded are determined. The solution is based on a volume integral equation and a statistical approach. The absorption coefficient of the array is found via the internal fields of the particles. The absorption coefficient of a matrix is found as the difference between the absorption coefficients of the composite structure and the particles. Numerical results are presented for arrays of metal, semiconductor, and dielectric nano- and microparticles of short-range order and imperfect long-range order in the absorbing media at normal and oblique incidence of a plane wave.