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.

Elastic Wave Scattering and Dynamic Stress Concentrations around Double Holes in Piezoelectric Media

In this paper, on the basis of Liu’s complex function and conformal mapping methods, supplemented by local coordinate system method, e-type piezoelectric material and elastic wave scattering and dynamic stress concentrations problems with double holes question are studied, and an analytical solution is given to the problems. On the basis of multiple scattering of elastic wave theory, put forward the study about microscopic dynamics model to dynamic stress in the structure of piezoelectric composites as well as dynamic playing field. As an example, the numerical results of the dynamic stress distribution around the hole in case double equal diameter holes are given in the paper, and the influence of incident wave number and hole-spacing parameters on the dynamic stress concentration factor is analyzed.

Using Refined Theory to Studied Elastic Wave Scattering and Dynamic Stress Concentrations in Plates with Two Cutouts

In this paper, based on complex variables and conformal mapping methods, using the refined dynamic equation of plates, elastic wave scattering and dynamic stress concentrations in plates with two cutouts were studied. Applying the orthogonal function expansion method, the problem to be solved can be reduced into the solution of a set of infinite algebraic equations. According to free boundary conditions, numerical results of dynamic moment concentration factors in thick plates with two circular cutouts analyze that: there will be more complex interaction changes between two-cutout situation than single cutout situation. In the case of low frequency or high frequency and thin plate, the hole-spacing in the absence of coupling interactions was larger or smaller. The numerical results and method can be used to analyze the dynamics and strength of plate-like structures.

ELASTIC WAVE SCATTERING AND DYNAMIC STRESS IN COMPOSITE WITH FIBER

Based on the theory of elastic dynamics, multiple scattering of elastic waves and dynamic stress concentrations in fiber_reinforced composite were studied. The analytical expressions of elastic waves in different region were presented and an analytic method to solve this problem was established. The mode coefficients of elastic waves were determined in accordance with the continuous conditions of displacement and stress on the boundary of the multi_interfaces. By making use of the addition theorem of Hankel functions, the formulations of scattered wave fields in different local coordinates were transformed into those in one local coordinate to determine the unknown coefficients and dynamic stress concentration factors. The influence of distance between two inclusions, material properties and structural size on the dynamic stress concentration factors near the interfaces was analyzed. It indicates in the analysis that distance between two inclusions, material properties and structural size has great influence on the dynamic properties of fiber_reinforced composite near the interfaces. As examples, the numerical results of dynamic stress concentration factors near the interfaces in a fiber_reinforced composite are presented and discussed.

Elastic Wave Scattering and Dynamic Stress Concentrations in Stretching Thick Plates with Two Cutouts by Using the Refined Dynamic Theory

Based on the refined dynamic equation of stretching plates, the elastic tensio compression wave scattering and dynamic stress concentrations in the thick plate with two cutouts are studied. In view of the problem that the shear stress is automatically satisfied under the free boundary condition, the generalized stress of the first-order vanishing moment of shear stress is considered. The numerical results indicate that, as the cutout is thick, the maximum value of the dynamic stress factor obtained using the refined dynamic theory is 19% higher than that from the solution of plane stress problems of elastic dynamics.

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.

The scattering of plane P1 wave by a 3-D sedimentary basin in a fluid-saturated poroelastic half-space using IBEM

The indirect boundary element method(IBEM)is applied to investigate the scattering of elastic waves around a 3-D sedimentary basin filled with fluid-saturated poroelastic medium.Based on this method,the free field and scattered field can be solved according to the boundary conditions.And the numerical accuracy has been verified.The effects of parameters on elastic wave scattering are studied,such as boundary condition,incident frequency,incident angle and porosity of medium.Numerical results illustrate that the amplification effect of surface displacement near poroelastic sedimentary basin is notable.In addition,for the case of large porosity the drainage condition has a significant impact on the response amplitude.Due to the fluid exchange at the interface under the drained condition,the displacement amplitude can be much larger than that under the undrained condition in present study.The study can provide a theoretical basis for the anti-seismic design of engineering structures located in sedimentary basin.

THE NYSTROM METHOD FOR ELASTIC WAVE SCATTERINGBY UNBOUNDED ROUGH SURFACES

We consider a numerical algorithm for the two-dimensional time-harmonic elastic wave scattering by unbounded rough surfaces with Dirichlet boundary condition.A Nystr¨om method is proposed for the scattering problem based on the integral equation method.Convergence of the Nystr¨om method is established with convergence rate depending on the smoothness of the rough surfaces.In doing so,a crucial role is played by analyzing the singularities of the kernels of the relevant boundary integral operators.Numerical experiments are presented to demonstrate the effectiveness of the method.Mathematics subject classification:35P25,45P05.

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.

Dynamic stress concentrations in thick plates with two holes based on refined theory

Based on complex variables and conformal mapping, the elastic wave scat- tering and dynamic stress concentrations in the plates with two holes are studied by the refined dynamic equation of plate bending. The problem to be solved is changed to a set of infinite algebraic equations by an orthogonM function expansion method. As examples, under free boundary conditions, the numerical results of the dynamic moment concen- tration factors in the plates with two circular holes are computed. The results indicate that the parameters such as the incident wave number, the thickness of plates, and the spacing between holes have great effects on the dynamic stress distributions. The results are accurate because the refined equation is derived without any engineering hypothese.

Analysis of the role of diffraction in topographic site effects using boundary element techniques

The role played by the diffraction field on the problem of seismic site effects is studied. For that purpose we solve and analyze simple scattering problems under P and SV in-plane wave assumptions, using two well known direct boundary-element-based numerical methods. After establishing the difference between scattered and diffracted motions, and introducing the concept of artificious and physically based incoming fields, we obtain the amplitude of the Fourier spectra for the diffracted part of the response： this is achieved after establishing the connection between the spatial distribution of the transfer function over the studied simple topographies and the diffracted field. From the numerical simulations it is observed that this diffracted part of the response is responsible for the amplification of the surface ground motions due to the geometric effect. Furthermore, it is also found that the diffraction field sets in a fingerprint of the topographic effect in the total ground motions. These conclusions are further supported by observations in the time-domain in terms of snapshots of the propagation patterns over the complete computational model. In this sense the geometric singularities are clearly identified as sources of diffraction and for the considered range of dimensionless frequencies it is evident that larger amplifications are obtained for the geometries containing a larger number of diffraction sources thus resulting in a stronger topographic effect. The need for closed-form solutions of canonical problems to construct a robust analysis method based on the diffraction field is identified.