Study on the Propagation and Focusing Mechanism of Long Waves over A Submerged Atoll

An analytical solution for long waves propagating over a submerged atoll is established. The atolls involved in this study are annular coral reefs with large lagoons in the middle, and the expression of the cross section is a trinomial function of the radial distance, i.e., h=ar(2s)-br~s+h_0, where s is the positive rational number. This analytical solution extends the theory by Wang et al.(2018) as s is no longer limited to s=2/m, where m is the positive integer. In addition, by adjusting the terrain parameters properly, the analytic solution can be degenerated to describe the wave propagation over topography with a hump or pit. According to the relationship between wave rays and wave energy, the distribution characteristics and formation mechanism of energy over the topography are expounded. When the lagoon is non-existent, all wave rays converge at the x-axis, which results in an abrupt amplification of the wave amplitude around the convergence point. When a lagoon is mounted on the top of the atoll, the rays are scattered due to the refraction of the lagoon, and only some rays converge at the symmetrical axis and the ridges on both sides,which results in the amplification of wave amplitudes in these areas.

A BOUNDARY ELEMENT METHOD FOR CALCULATING ELASTIC WAVES SCATTERED BY AXISYMMETRIC INCLUSION

A Boundary Element Method(BEM) is;described to compute the scattering of elastic waves by an axisymmetric inclusion in an infinite elastic medium. The boundary loads applied to the inclusion is expanded in terms of Fourier series in an infinite space. The boundary integral equation is solved in the general direction of the axisymmetric inclusion by BEM The problem of the 3-D scattering of elastic waves is reduced to a 1-D one. According to the geometric features of the axisymmetric inclusion the ring shell elements are adopted in this method. A comparison is made with other BEM methods. The numerical results show this method can reduce the amount of calculation and enhance the speed of convergence.

孔隙率对矩形沟槽上垂直多孔屏障的波浪散射效应影响

The effect of porosity on surface wave scattering by a vertical porous barrier over a rectangular trench is studied here under the assumption of linearized theory of water waves.The fluid region is divided into four subregions depending on the position of the barrier and the trench.Using the Havelock’s expansion of water wave potential in different regions along with suitable matching conditions at the interface of different regions,the problem is formulated in terms of three integral equations.Considering the edge conditions at the submerged end of the barrier and at the edges of the trench,these integral equations are solved using multi-term Galerkin approximation technique taking orthogonal Chebyshev’s polynomials and ultra-spherical Gegenbauer polynomial as its basis function and also simple polynomial as basis function.Using the solutions of the integral equations,the reflection coefficient,transmission coefficient,energy dissipation coefficient and horizontal wave force are determined and depicted graphically.It was observed that the rate of convergence of the Galerkin method in computing the reflection coefficient,considering special functions as basis function is more than the simple polynomial as basis function.The change of porous parameter of the barrier and variation of trench width and height significantly contribute to the change in the scattering coefficients and the hydrodynamic force.The present results are likely to play a crucial role in the analysis of surface wave propagation in oceans involving porous barrier over submarine trench.

Dynamic responses of a sediment-filled valley with a fluid layer subject to incident waves

The diffraction of elastic waves by a sedimentary valley in a homogeneous elastic half-space is studied in this paper. The sediment-filled valley is composed of a fluid layer over a soft soil deposit whose characteristics may be significant and should be carefully considered when designing long span bridges with high piers. The method of analysis adopted in the paper is to decompose the problem into an interior region and an exterior region. In the exterior region, the scattered wave fields are constructed with the linear combinations of two independent sets of Lamb＇s singular solutions, i.e., the integral solutions for two concentrated surface loads in two directions; and their derivatives are used to represent the scattered wave fields. A technique is proposed to calculate the integrals in the wave-number domain based on the method of steepest descent. For the interior region, the wave fields for the fluid layer and soft soil deposit are expressed in terms of wave functions which satisfy the equation of motion. The continuity condition at the interface of the media is satisfied in the least square sense. The effects of geometric topography, soil amplification and fluid layer subject to different types of incident harmonic plane waves are analyzed and discussed..

HALF-SPACE GREENS'S FUNCTION DUE TO A SPATIALLY HARMONIC LINE LOAD AND SCATTERED FIELDS IN THE FAR FIELD REGION

Half-space Green's function due to a spatially harmonic line load has been expressed as a sum of the full-space Green's functions and a 2-D integral representation of the reflected waves by the free surface of the half-space.By using the obtained half-space Green's function,an integral rep- resentation of the scattered waves by a cylindrical obstacle is then derived.Finally,by analyzing the far-zone behavior of the integrands of the integral representation.the far-field pattern of the scattered waves in a half-space obtained.

SCATTERING FAR FIELD SOLUTION OF SH-WAVE BY MOVABLE RIGID CYLINDRICAL INTERFACE INCLUSION

The Green's function is used to solve the scattering far fieldsolution of SH-wave by a mov- able rigid cylindrical interfaceinclusion in a linear elastic body. First, a suitable Green'sfunction is devel- oped, which is the fundamental displacementsolution of an elastic half space with a movable rigid half-cylin-drical inclusion impacted by out-of-plane harmonic line source loadedat any point of its horizontal surface.

SCATTERING OF FLEXURAL WAVES AND DYNAMIC STRESS CONCENTRATIONS IN MINDLIN'S THICK PLATES WITH A CUTOUT

Using the complex variable method and conformal mapping,scat- tering of flexural waves and dynamic stress concentrations in Mindlin's thick plates with a cutout have been studied.The general solution of the stress problem of the thick plate satisfying the boundary conditions on the contour of cutouts is obtained. Applying the orthogonal function expansion technique,the dynamic stress problem can be reduced into the solution of a set of infinite algebraic equations.As examples, numerical results for the dynamic stress concentration factor in Mindlin's plates with a circular,elliptic cutout are graphically presented in sequence.

Preliminary Discussion on the Relationship Between EM Wave Propagation Characteristics and Medium Parameters in Anisotropic Medium

The reflection and transmission characteristics of an anisotropic half-space medium normally illuminated by a plane wave are analyzed by kDB coordination. The general formula of reflection coefficient at the air-medium interface is given, and its validity is also discussed. The possible propagating modes in different mediums and the effect of medium parameters on these modes are emphatically studied. This work provides the theoretical preparations for the parameter reconstruction of an anisotropic material.

Diffraction of SH-waves by topographic features in a layered transversely isotropic half-space

Abstract： The scattering of plane SH-waves by topographic features in a layered transversely isotropic （TI） half-space is investigated by using an indirect boundary element method （IBEM）. Firstly, the anti-plane dynamic stiffness matrix of the layered TI half-space is established and the free fields are solved by using the direct stiffness method. Then, Green＇s functions are derived for uniformly distributed loads acting on an inclined line in a layered TI half-space and the scattered fields are constructed with the deduced Green＇s functions. Finally, the free fields are added to the scattered ones to obtain the global dynamic responses. The method is verified by comparing results with the published isotropic ones. Both the steady-state and transient dynamic responses are evaluated and discussed. Numerical results in the frequency domain show that surface motions for the TI media can be significantly different from those for the isotropic case, which are strongly dependent on the anisotropy property, incident angle and incident frequency. Results in the time domain show that the material anisotropy has important effects on the maximum duration and maximum amplitudes of the time histories.

SHEAR WAVE SCATTERING FROM A PARTIALLY DEBONDED PIEZOELECTRIC CYLINDRICAL INCLUSION

The scattering of SH wave by a cylindrical piezoelectric inclusion partially debonded from its surrounding piezoelectric material is investigated using the wave function expansion method and singular integral equation technique. The debonding regions are modeled as mul- tiple arc-shaped interface cracks with non-contacting faces. By expressing the scattered ?elds as wave function expansions with unknown coe?cients, the mixed boundary value problem is ?rstly reduced to a set of simultaneous dual series equations. Then dislocation density functions are introduced as unknowns to transform these dual series equations into Cauchy singular integral equations of the ?rst type, which can be numerically solved easily. The solution is valid for arbi- trary number and size of the debonds. Finally, numerical results of the dynamic stress intensity factors are presented for the cases of one debond and two debonds. The e?ects of incidence direc- tion, crack con?guration and various material parameters on the dynamic stress intensity factors are respectively discussed. The solution of this problem is expected to ?nd applications in the investigation of dynamic fracture properties of piezoelectric materials with cracks.

Wave Scattering by Double Slotted Barriers in A Steady Current:Experiments

The adoption of slotted breakwaters can be an ideal option in the protection of very large near-shore floating struc-trees that may extend offshore to a considerable water depth. In this paper, we experimently investigated the behaviour of wave transmission and reflection coefficients of double slotted barriers in the presence of a steady opposing current. The experimental results show that opposing currents have only minor effects on wave reflection, but can significantly reduce the wave transmission through double slotted barriers. The experimental results suggest that coastal currents should be taken into consideration for an economical design of slotted breakwaters.

A model for the scattering of long waves by slotted breakwaters in the presence of currents

Slotted breakwaters have been used to provide economical protection from waves in harbors where surface waves and currents may co-exist. In this paper, the effects of currents on the wave scattering by slotted breakwaters are investigated by using a simple model. The model is based on a long wave approximation. The effects of wave height, barrier geometry and current strength on the reflection and transmission coefficients are examined by the model. The model results are compared with recent experimental data. It is found that both the wave-following and wave-opposing currents can increase the reflection coefficient and reduce the transmission coefficient. The model can be used to study the interaction between long waves and slotted breakwaters in coastal waters.

scattering and refracting of plane strain wave by a cylindrical inclusion in fluidsaturated soils

The problems involving scattering and refracting of plane strain wave by a cylinder in fluidsaturated soils are studied in this paper. The theoretical solutions for the amplitudes of scattering and refracting are derived on the basis of modified Biot′s theory for twophase medium in engineering, in which the compressibility of soil grains and the viscous coupling effect between the skeletal frame and the pore fluid are taken into account. Moreover, the amplitude equations of potential function are presented when the fluidsaturated soil cylindrical inclusion is degenerated into cylindrical cavity, rigid cylinder, single phase elastic cylinder and single phase fluid cylinder.

Time domain method for calculating free field motion of a layered half-space subjected to obliquely incident body waves

In numerical simulation of wave scattering under oblique incident body waves using the finite element method, the free field motion at the incident lateral boundary induced by the background layered half-space complicates the computational area. In order to replace the complex frequency domain method, a time-domain method to calculate the free field motion of a layered half-space subjected to oblique incident body waves is developed in this paper. The new method decouples the equations of motion used in the finite element method and offers an interpolation formula of the free field motion. This formula is based on the fact that the apparent horizontal velocity of the free field motion is constant and can be calculated exactly. Both the theoretical analysis and numerical results demonstrate that the proposed method offers a high degree of accuracy.

Elastic Wave Scattering by Two-Dimensional Periodical Array of Cylinders

We extend the multiple-scattering theory (MST) for elastic wave scattering and propagating in two-dimensional composite. The formalism for the band structure calculation is presented by taking into account the full vector character of the elastic wave. As a demonstration of application of the formalism we calculate the band structure of elastic wave propagating in a two-dimensional periodic arrangement of cylinders. The results manifest that the MST shows great promise in complementing the plane-wave (PW) approach for the study of elastic wave.

SCATTERING OF ELASTIC WAVES IN AN ELASTIC MATRIX CONTAINING AN INCLUSION WITH INTERFACES

Based on the theory of elastic dynamics, the scattering of elasticwaves and dynamic stress concentration of fiber-reinforced compositewith interfaces are studied. Analytical expressions of elastic wavesin different medium areas are presented and an analytic method ofsolving this problem is established. The mode coefficients aredetermined by means of the continuous conditions of displacement andstress on the boundary of the interfaces. The influence of materialproperties and structural size on the dynamic stress con- centrationfactors near the interfaces is analyzed.

DYNAMIC ANALYSIS OF A BURIED RIGID ELLIPTIC CYLINDER PARTIALLY DEBONDED FROM SURROUNDING MATRIX UNDER SHEAR WAVES

This paper investigates the dynamic behavior of a buried rigid elliptic cylinder partially debonded from surrounding matrix under the action of anti-plane shear waves (SH waves). The debonding region is modeled as an elliptic arc-shaped interface crack with non-contacting faces. By using the wave function (Mathieu function) expansion method and introducing the dislocation density function as an unknown variable, the problem is reduced to a singular integral equation which is solved numerically to calculate the near and far fields of the problem. The resonance of the structure and the effects of various parameters on the resonance are discussed.

Scattering of Circularly Polarized Terahertz Waves on a Graphene Nanoantenna

We present a surface current method to model the graphene rectangular nanoantenna scattering in the terahertz band with Comsol. Compared with the equivalent thin slab method, the results obtained by the surface current method are more accurate and efficient. Then the electromagnetic scattering of circularly polarized terahertz waves on graphene nanoantennas is numerically analyzed by utilizing the surface current method. The depen- dences of the antenna resonant frequency with the circularly polarized wave on width and length are consistent with those for the linear polarized waves. These results are proved to be useful to design et^cient nanoantennas in terahertz wireless communications.

Scattering of seismic waves by three-dimensional large-scale hill topography simulated by a fast parallel IBEM

To solve seismic wave scattering by a large-scale three-dimensional(3-D) hill topography, a fast parallel indirect boundary element method(IBEM) is developed by proposing a new construction method for the wave field, modifying the generalized minimum residual(GMRES) algorithm and constructing an Open MP plus MPI parallel model. The validations of accuracy and efficiency show that this method can solve 3-D seismic response of a large-scale hill topography for broadband waves, and overcome the weakness of large storage and low efficiency of the traditional IBEM. Based on this new algorithm architecture, taking the broadband scattering of plane SV waves by a large-scale Gaussian-shaped hill of thousands-meters height as an example, the influence of several important parameters is investigated, including the incident frequency, the incident angle and the height-width and length-width ratio of the hill. The numerical results illustrate that the amplification effect on the ground motion by a near-hemispherical hill is more significant than the narrow hill. For low-frequency waves, the scattering effect of the higher hill is more pronounced, and there is only a single peak near the top of the hill. However, for high-frequency waves, rapid spatial variation of displacement amplitude appears on the hill surface.

A Linear Theory for Wave Scattering by Double Slotted Barriers in Weak Steady Currents

Recent experimental results have shown that the presence of a steady current can significantly reduce the energy of transmitted waves. In this paper, a theory is developed to study the wave scattering by single or double vertical slotted barriers in the presence of a weak uniform current. The quasi-linear theory is based on an eigenfunction expansion method. Comparisons between theory and existing experimental results for both single slotted barrier and double slotted barriers show satisfactory agreements. In consideration of wave propagation in a weak current it is found that the friction factor used to characterize the head loss at the slotted barrier depends on both the geometry of the slotted barrier and the strength of the steady current.