Reconfigurable mechanism-based metamaterials for ternary-coded elastic wave polarizers and programmable refraction control

Elastic metamaterials with unusual elastic properties offer unprecedented ways to modulate the polarization and propagation of elastic waves.However,most of them rely on the resonant structural components,and thus are frequency-dependent and unchangeable.Here,we present a reconfigurable 2D mechanism-based metamaterial which possesses transformable and frequency-independent elastic properties.Based on the proposed mechanism-based metamaterial,interesting functionalities,such as ternarycoded elastic wave polarizer and programmable refraction,are demonstrated.Particularly,unique ternary-coded polarizers,with 1-trit polarization filtering and 2-trit polarization separating of longitudinal and transverse waves,are first achieved.Then,the strong anisotropy of the proposed metamaterial is harnessed to realize positive-negative bi-refraction,only-positive refraction,and only-negative refraction.Finally,the wave functions with detailed microstructures are numerically verified.

Reflection and refraction of attenuated waves at boundary of elastic solid and porous solid saturated with two immiscible viscous fluids

The propagation of elastic waves is studied in a porous solid saturated with two immiscible viscous fluids. The propagation of three longitudinal waves is represented through three scalar potential functions. The lone transverse wave is presented by a vector potential function. The displacements of particles in different phases of the aggregate are defined in terms of these potential functions. It is shown that there exist three longitudinal waves and one transverse wave. The phenomena of reflection and refraction due to longitudinal and transverse waves at a plane interface between an elastic solid half-space and a porous solid half-space saturated with two immiscible viscous fluids are investigated. For the presence of viscosity in pore-fluids, the waves refracted to the porous medium attenuate in the direction normal to the interface. The ratios of the amplitudes of the reflected and refracted waves to that of the incident wave are calculated as a non- singular system of linear algebraic equations. These amplitude ratios are used to further calculate the shares of different scattered waves in the energy of the incident wave. The modulus of the amplitude and the energy ratios with the angle of incidence are computed for a particular numerical model. The conservation of the energy across the interface is verified. The effects of variations in non-wet saturation of pores and frequencies on the energy partition are depicted graphically and discussed,

Reflection and refraction of plane waves at the boundary of an elastic solid and double-porosity dual-permeability materials

Phenomena of reflection and refraction of plane harmonic waves at a plane interface between an elastic solid and doubleporosity dual-permeability material are investigated. The elastic solid behaves non-dissipatively, while double-porosity dual-permeability materials behave dissipatively to wave propagation due to the presence of viscosity in pore fluids. All the waves(i.e., incident and reflected) in an elastic medium are considered as homogeneous(i.e., having the same directions of propagation and attenuation), while all the refracted waves in double-porosity dual-permeability materials are inhomogeneous(i.e., having different directions of propagation and attenuation). The coefficients of reflection and refraction for a given incident wave are obtained as a non-singular system of linear equations. The energy shares of reflected and refracted waves are obtained in the form of an energy matrix. A numerical example is considered to calculate the partition of incident energy among various reflected and refracted waves. The effect of incident direction on the partition of the incident energy is analyzed with a change in wave frequency, wave-induced fluid-flow, pore-fluid viscosity and double-porosity structure.It has been confirmed from numerical interpretation that during the reflection/refraction process, conservation of incident energy is obtained at each angle of incidence.

Mathematical Models for Combined Refraction-Diffraction of Waves on Non-Uniform Current and Depth

Two mathematical models for combined refraction-diffraction of regular and irregular waves on non-uniform current in water of slowly varying topography are presented in this paper. Model I is derived by wave theory and variational principle separately. It has two kinds of expressions including the dissipation term. Model n is based on the energy conservation equation with energy flux through the wave crest lines in orthogonal curvilinear coordinates and the wave kinematic conservation equation. The analysis and comparison and special cases of these two models are also given.

Numerical Simulation for Refraction-Diffraction of Waves in Water of Slowly Varying Current and Topography

A new numerical finite difference iteration method for refraction-diffraction of waves ia water of slowly varying current and topography is developed in this paper. And corresponding theoretical model including the dissipation term is briefly described, together with some analysis and comparison of computational results of the model with measurements in a hydraulic scale model (Berkhoff et al., 1982). An example of practical use of the method is given, showing that the present model is useful to engineering practice.

Reflection and refraction of waves in oscillatory media

This paper uses the two-dimensional Brusselator model to study reflection and refraction of chemical waves. It presents some boundary conditions of chemical waves, with which occurence of observed phenomena at interface as refraction and reflection of chemical waves can be interpreted. Moreover, the angle of reflection may be calculated by using the boundary conditions. It finds that reflection and refraction of chemical waves can occur simultaneously even if plane wave goes from a medium with higher speed to a medium with lower speed, provided the incident angle is larger than the critical angle.

The Mathematical Modelling for Studying the Influence of the Initial Stresses and Relaxation Times on Reflection and Refraction Waves in Piezothermoelastic Half-Space

The present paper concentrates on the study of reflection and refraction phenomena of waves in pyroelectric and piezo-electric media under initial stresses and two relaxation times influence by apply suitable conditions. The generalized theories of linear piezo-thermoelasticity have been employed to investigate the problem. In two-dimensional model of transversely isotropic piezothermoelastic medium, there are four types of plane waves quasi-longitudinal (qP), quasi-transverse (qSV), thermal wave (T-mode), and potential electric waves (φ-mode) The amplitude ratios of reflection and refraction waves have been obtained. Finally, the results in each case are presented graphically.

Asymmetry in Negative Refraction of Nonlinear Waves

Recently, inwardly propagating waves （called antiwaves, AWs） in nonlinear oscillatory systems have attracted much attention. An interesting negative refraction phenomenon has been observed in a bidomain system where one medium supports forwardly propagating waves （normal waves, NWs） and the other AWs. In this paper we find that negative refraction （NR） in nonlinear media has an asymmetric property, i.e., NR can be observed only by applying wave source with proper frequency to one medium, but not the other. Moreover, NR appears always when the incident waves are dense and the refractional waves are sparse. This asymmetry is a particular feature for nonlinear NR, which can neither be observed in linear refraction processes （both positive and negative refractions） nor in nonlinear positive refraction. The mechanism underlying the asymmetry of nonlinear NR are fully understood based on the competition of nonlinear waves.

Refraction-Diffraction Mathematical Model for Waves With Lateral Energy Transmission Mechanism and Its Verification

To solve problems concerning wave elements and wave propagation, an effective way is the wave energy balance equation, which is widely applied in oceanography and ocean dynamics for its simple computation. The present papaer advances wave energy balance equations considering lateral energy transmission and energy loss as the governing equation for the study of wave refraction-diffraction. For the mathematical model, numerical simulation is made by means of difference method, and the result is verified with two examples.

Combined refraction and diffraction models for sea waves over complicated topography and with currents in shallow water

-Combined refraction and diffraction models in the form of linear parabolic approximation are derived through smallparameter method. More strictly theoretical basis and more accuracy in the models than Lozano's (1980) are obtained. Some theoretical defects in Liu's model (1985) with consideration of current are not only found but also eliminated. More strict and accurate models are, therefore, presented in this paper.The calculation results and analysis in applying the models to actual wave field with consideration of bottom friction will be given in the following paper.

A COMBINED REFRACTION-DIFFRACTION-DISSIPATION MODEL OF WAVE PROPAGATION

A numerical model based on the mild-slope equation of water wave propagation over complicated bathymetry,taking into account the combined effects of refraction,diffraction and dissipation due to wavebreaking is presented.Wave breaking is simulated by modifying the wave height probability density func-tion and the wave energy dissipation mechanism is parameterized according to that of the hydraulic jumpformulation.Solutions of the wave height,phase function,and the wave direction at every grid point areobtained by finite difference approximation of the governing equations,using Gauss-Seidel Iterative Method(GSIM)row by row.Its computational convenience allows it to be applied to large coast regions tostudy the wave transformation problem.Several case studies have been made and the results compare verywell with the experiment data and other model solutions.The capability and utility of the model forreal coast areas are illustrated by application to a shallow bay of northeast Australia.

Water Wave Refraction and Diffraction over Frictional Topography

This paper considers the effect of wave energy dissipation induced by sea-bottom friction on the computational results of water wave refraction and diffraction with the parabolic equation method. The presented results show that the friction factor formula adopted in this paper is of higher numerical accuracy than that introduced by Dalrymphe (1984), and it can be used to compute wave propagation over large open areas.

Wave measurement based on light refraction

Some authors have developed a few methods of measuring wave slopes based on light refraction, including the measurement method via the distribution of light intensity or color under water. A new method based on light refraction is specified for the measurement of wave surface elevation in wave flume via imaging technology. A plane painted with black and white stripes is put on the flume floor as an indication plane, which can be arranged easily and cheaply. Compared with the previous methods, the present method is less sensitive to the noise and nonlinear effects of optical process, which can be taken as a digital method. The CCD camera is fixed above the flume with its optical axis arranged vertically to grab the images of stripes modulated by the wave surface. The modulated value can be calculated from the Hilbert transform, and then the wave surface elevation can be obtained. The algorithm and experimental procedure are specified in detail, and some experimental results are provided to show the validity of the present method.

Influence of Energy Directional Spread on Wave Spectral Refraction

Pierson- Moskowitz Spectrum, JONSWAP Spectrum as well as Bretschneider- Mitsuyasu Spectrum are used in this paper for analyzing the influence of wave energy directional spread on refraction of wave spectrum due to both current and topography of sea bed. The author's calculation indicates that such kind influence on the characteristic value of wave height as well as the average direction of wave energy propagation can not be ignored.

Cavity effect on Rayleigh wave dispersion and P-wave refraction

Sinkholes and cavities can represent serious hazards to human safety and urban infrastructures,cause roadbed subsidence,and so on.It is therefore essential to evaluate various sinkholes in different depths and sizes to assess the risk of collapse.This paper evaluates the effect of different cavities on Rayleigh-wave propagation and body(P)wave refraction.Rayleigh(R)wave propagation is analyzed according to the classical multi-channel analysis of surface waves(MASW)method also considering the R-wave backscattering.Synthetic seismic traces are computed by means of finite element modeling(FEM)for cavity and intrusion at different depths and sizes.Furthermore,field acquisition data is used to verify the detection effect of a cavity on R-and P-waves.The results show that the presence of backscattered R-waves and the changes in the R-wave velocity spectrum can help in cavity identification.Additional possible evidence is represented by significant changes in the refraction travel times over the cavity location.It can be concluded that the field data are in good agreement with the synthetic,and it could be effective to consider the results of both R-and P-wave analysis in order to efficiently identify the cavities.

Numerical Modeling of Wave Diffraction-Refraction in Water of Varying Current and Topography

A numerical model for wave diffracrion-refraction in water of varying current and topography is proposed, and time-dependent wave mild-slope equation with a dissipation term and corresponding equivalent: governing equations are presented. Two different expressions of parabolic approximations for the case of the absence of current are also given and analyzed. The influence of current on the results of simulation of waves is discussed. Some examples show that the present model is better than others in simulating wave transformation in large water areas. And they also show that the influence of current should be taken into account, on numerical modeling of wave propagation in water of strong current and coastal areas, otherwise the modeling results will be largely distorted.

Research on Temperature Field Reconstruction Based on RBF Approximation with Polynomial Reproduction Considering the Refraction Effect of Sound Wave Paths

The temperature field distribution directly reflects the combustion condition in a furnace.In this paper,acoustic thermometry to reconstruct temperature distribution is investigated.A method based on radial basis function approximation with polynomial reproduction(RBF-PR)is proposed in order to improve the accuracy and stability of the method based on RBF approximation.In addition,the refraction effect of sound wave paths is considered in the process of reconstruction.The curved lines with refraction effect are numerically calculated by solving differential equations,which show that sonic waves curve towards the zones of higher temperature.The reconstructed performance is validated via numerical simulation using four temperature distribution models.Results and analysis show that the proposed method has much greater accuracy than the method based on RBF approximation,and when considering the effect of refraction,our method can reconstruct more excellent reconstruction performance than others,which do not take into account the refraction effect of sound wave paths.

Validity of the Refraction Microtremors (ReMi) Method for Determining Shear Wave Velocities for Different Soil Types in Egypt

The Refraction Microtremor (ReMi) method is being used around the world by the geotechnical and geophysical community to determine shear-wave velocities. This is due to its faster, less expensive and accurate determination of shear wave velocities, when compared to other methods used. Unlike standard crosshole and downhole techniques, ReMi does not require any drilling. It eliminates the problem of shear-wave source and quiet site that are pre-requisites for good seismic refraction surveys. In this paper we present refraction microtremors (ReMi) measurements done at sites underlain by different soil types in Egypt. The ReMi data were collected using standard refraction equipment employing 12, 24 or 48 channels. We used deep oceanographic noise and ambient noise including energy from power generators, pile drivers and traffic. The data were processed using the SeisOpt? ReMi? (? Optim, Inc.) software to reveal one-dimensional shear-wave velocity structures beneath the arrays. To access the validity of the method for the Egyptian soils, the shear-wave profiles obtained from the ReMi measurements were compared to downhole and crosshole data for different soils. Comparisons demonstrate the robustness of the ReMi technique for obtaining shear-wave velocities for different soil types in Egypt.

An interpretation of wave refraction and its influence on foreshore sediment distribution

To analyze the grain size and depositional environment of the foreshore sediments, a study was undertaken on wave refraction along the wide sandy beaches of central Tamil Nadu coast. The nearshore waves approach the coast at 45° during the northeast(NE) monsoon, at 135° during the southwest(SW) monsoon and at 90° during the non-monsoon or fair-weather period with a predominant wave period of 8 and 10 s. A computer based wave refraction pattern is constructed to evaluate the trajectories of shoreward propagating waves along the coast in different seasons. The convergent wave rays during NE monsoon, leads to high energy wave condition which conveys a continuous erosion at foreshore region while divergent and inept condition of rays during the SW and non-monsoon, leads to moderate and less energy waves that clearly demarcates the rebuilt beach sediments through littoral sediment transport. The role of wave refraction in foreshore deposits was understood by grain size and depositional environment analysis. The presence of fine grains with the mixed population, during the NE monsoon reveals that the high energy wave condition and sediments were derived from beach and river environment. Conversely, the presence of medium grains with uniform population, during SW and non-monsoon attested less turbulence and sediments were derived from prolong propagation of onshore-offshore wave process.These upshots are apparently correlated with the in situ beach condition. On the whole, from this study it is understood that beaches underwent erosion during the NE monsoon and restored its original condition during the SW and non-monsoon seasons that exposed the stability of the beach and nearshore condition.

Computation of Wave Refraction-Diffraction with Error Vector Propagation Method

After modifying the basic computation model made by Panchang (1988), the error vector propagation (EVP) method has been adopted to compute the combined effects of water wave refraction and diffraction in the presence of reflection boundary. The results show that the present method is successful in restraining the noise in Panchang's solution. Compared to other numerical methods for the mild-slope wave equation, EVP method can both consider the influence of reflection and save computer memory and computing time.