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The development of seismic metamaterials (SMs) offers a novel approach for isolating seismic waves. Nevertheless, achieving a broad low-frequency band gap within a compact structure remains a challenging issue that requires further resolution. To address this challenge, the study introduces a chiral structure into SMs. The designed chiral seismic metamaterial structure (CSMS) comprises four commonly used construction materials: soil, steel, rubber, and aluminum. The band structure, along with the sound cone, is explored through the application of the finite element method. The influence of geometric configurations and material properties on the band gaps is examined. In particular, the impacts of the count and curvature of the ligaments in the chiral structure on the band gap are investigated. The findings indicate that geometric and material parameters exert a substantial influence on the band gaps. The vibration energy is mainly concentrated in the chiral structure. Both Love and Rayleigh waves can be effectively attenuated within the band gaps, while seismic waves outside the band gaps cannot be attenuated effectively. Furthermore, the analysis of the frequency domain and time domain further validates the vibration-damping efficacy of the proposed structures in real earthquakes. Therefore, it can be concluded that low-frequency broadband gaps can be obtained to effectively control seismic wave propagation when a chiral structure is incorporated into SMs. The findings of this study can offer a theoretical basis for the application of chiral structures in SMs.

Highly efficient coupling outer electromagnetic (EM) waves into photonic crystal (PhC) waveguides (PhCWs) is critical to the applications of PhCs in photonic integrated circuits. We investigate and simulate an efficient way of coupling EM waves into PhCWs of air holes array by using surface dielectric margin based on all-PhCs structure. Good matching of modal field profiles on both sides of the interface is obtained by adjusting the surface dielectric margin along the propagation direction. The coupling efficiency can be highly enhanced by suppressing the surface field propagating along the transverse margin at the interface. The numerical results using finite-difference time-domain simulations show that the bandwidth for coupling efficiency larger than 90% can be as broad as about 100nm.

We analyze the localization in three-layered symmetric structure consisting of linear layer between focusing nonlinear media separated by nonlinear interfaces. The mathematical formulation of the model is a one-dimensional boundary value problem for the nonlinear Schrödinger equation. We find nonlinear localized states of two types of symmetry. We derive the energies of obtained stationary states in explicit form. We obtain the localization energies as exact solutions of dispersion equations choosing the amplitude of the interface oscillations as a free parameter. We analyze the conditions of their existence depending on the combination of signs of interface parameters.

Proper Orthogonal Decomposition (POD) was used as a suitable tool to characterize the evolution of fingers regime in Faraday instability. The transition from harmonic to subharmonic resonant finger behavior was thus studied. A cluster algorithm and Voronoi neighbor statistics were used to characterize the surface peak distribution for the principal spatial pattern. The structural transition was analyzed for varying acceleration amplitude used as system control parameter.

In this paper we consider a system of integrodifferential equations describing, in a long wave approximation, plane-parallel rotational motions of an ideal incompressible liquid with a free surface. Using special identities, we calculate integral Riemann invariants which are conserved along the trajectories and characteristics. A new class of solutions for this system is found. The description of these special solutions simplifies essentially since in this case the integrodifferential system reduces to a hyperbolic system of two differential equations admitting formulation in the Riemann invariants. The solutions describing propagation of simple waves are obtained in an analytical form. Numerical simulations of rotational flows are performed using both the system describing the special class of the solutions and shallow water equations for rotational flows. In order to describe discontinuous rotational flows, the equations of motion are written in a special conservation form and jump conditions are derived. A non-oscillatory, second-order central scheme is used in the calculations. Some illustrative solutions are presented for smooth and discontinuous rotational flows.

The paper is devoted to modeling of the backscattered field from a spherical target immersed in a homogeneous waveguide covered with ice. A bottom of the waveguide and an ice cover are fluid, attenuating half-spaces. A target is assumed to be acoustically rigid or fluid. In particular, the properties of the ice cover and a scatterer may coincide. The emitted signal is a pulse with a Gaussian envelope. The normal mode evaluation is applied to the scattering coefficients of a sphere. The amount of normal modes forming the backscattered field is determined by a given directivity of the source. Computational results are obtained in a wide frequency range 8–12kHz for water depths equal to several hundreds of meters, and distances between a source/receiver and a target from 1km up to 10km. It is shown that in a range interval up to several kilometers the backscattered field can be calculated also using a simplified medium model consisting of a water half-space and an ice half-space. In this case the scattering coefficients of a sphere are evaluated by the steepest descent method. For the considered oceanic waveguide of 200m depth with a sandy bottom the use of the simplified medium model essentially shortens a computing time.

Localization of surface plasmons polariton is reviewed in the context of experiments and modeling of near-field optical images. Near-field imaging of elastic (in-plane) surface plasmon scattering is discussed, and approaches for the correct image interpretation are outlined. Nonlinear effects related to localized surface plasmons are pressented. Surface plasmon localization opens up numerous possibilities for application in biosensing, nanophotonics, and in general in the area of surface optics properties.

The recent theoretical predictions and experimental observations of discrete surface solitons propagating along the interface between a one- or two-dimensional continuous medium and a one- or two-dimensional waveguide array are reviewed. These discrete solitons were found in second order (periodically poled lithium niobate) and third order nonlinear media, including AlGaAs, photorefractive media and glass, respectively.

This paper is concerned with a two-dimensional Whitham–Boussinesq system modeling surface waves of an inviscid incompressible fluid layer. We prove that the associated Cauchy problem is well-posed for initial data of low regularity, with existence time of scale ${𝒪}({\mu }^{3/2-}{𝜖}^{-2+})$, where $\mu$ and $𝜖$ are small parameters related to the level of dispersion and nonlinearity, respectively. In particular, in the KdV regime $\{\mu \sim 𝜖$}, the existence time is of order ${𝜖}^{-1/2}$. The main ingredients in the proof are frequency loacalized dispersive estimates and bilinear Strichartz estimates that depend on the parameter $\mu$.

Two novel seismic metamaterials models, trophy and apple core, inspired by an ancient Chinese puzzle are proposed in this study. Bandgaps below 15Hz are achieved by exclusively using concrete as the base material in the designs. Vibration modes are investigated to clarify the bandgap formation. Through comparison, we found that under the same volume, the apple core model can provide a lower frequency bandgap than the trophy model. Results from transient simulations and band structures are in good agreement, validating the accuracy of the simulation results. To broaden the bandwidth, the radii of the apple core models are varied and arranged in a gradient pattern. Transient analyses using a Gaussian wave packet and Taiwan’s Chi-Chi earthquake dataset are conducted to verify the effectiveness of the gradient apple core seismic metamaterial.

Rayleigh-type surface waves propagating in an incompressible isotropic half-space of nonconducting magnetoelastic material are studied for a half-space subjected to a finite pure homogeneous strain and a uniform magnetic field. First, the equations and boundary conditions governing linearized incremental motions superimposed on an initial motion and underlying electromagnetic field are derived and then specialized to the quasimagnetostatic approximation. The magnetoelastic material properties are characterized in terms of a "total" isotropic energy density function that depends on both the deformation and a Lagrangian measure of the magnetic induction. The problem of surface wave propagation is then analyzed for different directions of the initial magnetic field and for a simple constitutive model of a magnetoelastic material in order to evaluate the combined effect of the finite deformation and magnetic field on the surface wave speed. It is found that a magnetic field in the considered (sagittal) plane in general destabilizes the material compared with the situation in the absence of a magnetic field, and a magnetic field applied in the direction of wave propagation is more destabilizing than that applied perpendicular to it.

The objective of this paper is to investigate the surface waves in fiber-reinforced anisotropic elastic medium subjected to magnetic and thermal fields. We introduce the coupled theory (CD), Lord–Shulman (LS) theory and Green–Lindsay (GL) theory to study the influence of magnetic field on 2D problem of a fiber-reinforced thermoelastic. The analytical expressions for displacement components and force stress are obtained in the physical domain by using the harmonic vibrations. The wave velocity equations have been obtained in different cases. Numerical results for the temperature, displacement, and thermal stress components are given and illustrated graphically in the presence and absence of the magnetic field of the material medium. A comparison is also made between the three theories in the case of presence and absence of fiber-reinforced parameters.

Surface waves have been extensively studied in earthquake seismology. Surface waves are trapped near an infinitely large surface. The displacements decay exponentially with depth. These waves are also named Rayleigh and Love waves. Surface waves are also used for nondestructive testing of surface defects. Similar waves exist in finite width three-dimensional plates. In this case, displacements are no longer constant in the direction perpendicular to the wave propagation plane. Wave energy could still be trapped near the edge of the three-dimensional plate, and hence the term edge waves. These waves are thus different to the two-dimensional Rayleigh and Love waves. This paper presents a numerical model to study dispersion properties of edge waves in plates. A two-dimensional semi-analytical finite element method is developed, and the problem is closed by a perfectly matched layer adjacent to the edge. The numerical model is validated by comparing with available analytical and numerical solutions in the literature. On this basis, higher order edge waves and mode shapes are presented for a three-dimensional plate. The characteristics of the presented edge wave modes could be used in nondestructive testing applications.

An analytical-numerical method is proposed to analyze the surface waves in multi-layered piezoelectric cylinders. In this present method, the cylinder is divided into layer elements with three-nodal-lines along the wall thickness. The Hamilton principle is used to develop approximate dynamic equilibrium equations. The dispersion relationship for multi-layered cylinder is defined and deduced from the Rayleigh quotient and the orthogonal condition of the eigenvalues. The method of Fourier transform combined with the modal analysis is used to determine the displacement response and electronic potential to mechanical and electromechanical loads. Numerical examples are presented for calculating the frequency and group velocity dispersion behaviors, as well as electronic potential distribution in multi-layered piezoelectric cylinder.

Existing models for wave-related (cross-shore) sand transport are primarily based on data from oscillatory flow tunnel experiments. However, theory and former experiments indicate that flow differences between full scale surface waves and oscillatory flow tunnels may have a substantial effect on the net sand transport. In this paper, high resolution measurements of both boundary layer flow characteristics and net sand transport rates under full scale surface waves are presented. These experiments were performed for different wave conditions with medium (D₅₀ = 0.25 mm) and fine (D₅₀ = 0.14 mm) sand. It is shown that, especially under sheet-flow conditions, small wave induced net currents are of large importance for sand transport rates.