scholarly journals Scattering of Antiplane SH Waves by Complex Landforms

2021 ◽  
Vol 2021 ◽  
pp. 1-21
Author(s):  
Menghan Sun ◽  
Hui Qi
Keyword(s):  
Incident Angle ◽  
Complex Function ◽  
Surface Displacement ◽  
Complex Model ◽  
Barrier Effect ◽  
Algebraic Equations ◽  
Multiple Reflections ◽  
Sh Waves ◽  
Order Bessel Function ◽  
Incident Frequency

The multiple scattering of SH waves by isosceles triangular hill, semicircle depression, and isosceles trapezoidal hill in the solid half-space is studied. The complex model is divided into multiple subdomains by using the region matching method, then the wave functions in each subdomain are constructed by using the fractional-order Bessel function, and finally, the infinite algebraic equations for solving the unknown coefficients in the wave function are established by using the multipolar coordinate technique and the complex function method according to the boundary conditions. Fourier series is used to solve the unknown undetermined coefficients. The results show that due to the multiple reflections of the incident wave between complex landforms, surface displacement amplitude is affected by the incident angle, incident frequency, and the distance between the isosceles triangular hill, semicircle depression, and isosceles trapezoidal hill. It is found that when the incident frequency increases, there is a certain amplification effect between the hills and the depression. When the wave is incident horizontally, there is a certain “barrier” effect between hills and depression, and when the distance between the hills and depression reaches a certain level, the “barrier” effect will reach a stable value.

scholarly journals Scattering of SH Waves by a Partially Debonded Cylindrical Inclusion in the Covering Layer

2020 ◽  
Vol 2020 ◽  
pp. 1-13
Author(s):  
Hui Qi ◽  
Yang Zhang ◽  
Fuqing Chu ◽  
Jing Guo
Keyword(s):  
Stress Concentration ◽  
Dynamic Stress ◽  
Complex Function ◽  
Surface Displacement ◽  
Expansion Method ◽  
Cylindrical Inclusion ◽  
Dynamic Stress Concentration ◽  
Sh Waves ◽  
Covering Layer ◽  
The Impact

This article presents analytical solutions to the problem of dynamic stress concentration and the surface displacement of a partially debonded cylindrical inclusion in the covering layer under the action of a steady-state horizontally polarized shear wave (SH wave); these solutions are using the complex function method and wave function expansion method. By applying the large-arc assumption method, the straight line boundary of the half-space covering layer is transformed into a curved boundary. The wave field of the debonded inclusion is constructed utilizing a Fourier series and boundary conditions of continuity. The impact of debonding upon the dynamic stress concentration and surface displacement around the cylindrical concrete or steel inclusion is analyzed through numerical examples of the SH waves that are incident at normal angles, from a harder medium to a softer medium and from a softer medium to a harder medium. The examples show that various factors (including the medium parameters of the soil layers and the inclusion, the frequency of the incident waves, and the debonding situations) jointly affect the dynamic stress concentration factor and the surface displacement around the structure.

Scattering of Subsurface Cylindrical Cavity near Multiple Semi-Cylindrical Alluvial Valleys under Incident SH-Waves

2011 ◽  
Vol 374-377 ◽  
pp. 1285-1290
Author(s):  
Hui Wen Wang ◽  
Xiao Juan Sun ◽  
Zai Lin Yang
Keyword(s):  
Cylindrical Cavity ◽  
Complex Function ◽  
Auxiliary Function ◽  
Elastic Half Space ◽  
Continuity Condition ◽  
Polar Coordinates ◽  
Wave Number ◽  
Algebraic Equations ◽  
Sh Waves ◽  
Incident Waves

The scattering of subsurface cylindrical cavity near multiple semi-cylindrical alluvial valleys under incident SH waves is studied in this paper by using methods of auxiliary function, complex function multi-polar coordinates. The model is divided into two parts, Domain I is multiple semi-cylindrical alluvial valleys, and Domain Ⅱ is an elastic half space with several subsurface circular cavities near multiple semi-cylindrical alluvial valleys. A series of infinite algebraic equations is then obtained based on the displacement and stress continuity condition on “common boundary” of two parts after constructing the associated displacement and stresses expressions of each part. Numerical examples illustrate that material parameters of semi-cylindrical alluvial valleys have great impact on DSCF around subsurface cavity and DSCF dose not always decrease as wave number increases especially under incident waves with high frequency when the alluvial valleys are “softer”.

Dynamic Stress Concentration Analysis of Multiple Circular Cavities near Multiple Semi-Cylindrical Alluvial Valleys

2011 ◽  
Vol 121-126 ◽  
pp. 3253-3257
Author(s):  
Hui Wen Wang ◽  
Zai Lin Yang ◽  
Hua Nan Xu
Keyword(s):  
Dynamic Response ◽  
Complex Function ◽  
Elastic Half Space ◽  
Continuity Condition ◽  
Polar Coordinates ◽  
Algebraic Equations ◽  
Sh Waves ◽  
Common Boundary ◽  
Incident Plane ◽  
Domain I

The problem of dynamic response of multiple circular cavities near multiple semi-cylindrical alluvial valleys under incident plane SH-waves is investigated by the methods of complex function and multi-polar coordinates in this paper. Firstly, the solution domain is divided into two parts, Domain I is multiple semi-cylindrical alluvial valleys, and Domain Ⅱ is an elastic half space with several subsurface circular cavities near multiple semi-cylindrical alluvial valleys. A series of infinite algebraic equations is then obtained based on the displacement and stress continuity condition on “common boundary” of two parts after constructing the associated displacement and stresses expressions of each part. Finally some numerical expamples are prensented and dynamic response of subsurface circular cavities near semi-cylindrical alluvial valleys with respect to different parameters is discussed.

A study on the scattering field of SH-waves in a topographical area consisting of a semi-cylindrical hill and a subsurface horizontal hole

2007 ◽  
Vol 221 (3) ◽  
pp. 451-465 ◽  
Author(s):  
G Wang ◽  
L Dai ◽  
D Liu
Keyword(s):  
Stress Condition ◽  
Numerical Solutions ◽  
Complex Function ◽  
Algebraic Equations ◽  
Sh Wave ◽  
Sh Waves ◽  
Linear Algebraic Equations ◽  
Scattering Field ◽  
Moving Coordinate ◽  
Infinite Linear

This research intends to investigate the scattering field of SH-wave in a half-space containing a semicylindrical hill and a subsurface horizontal hole. A mathematical model is established in a two-dimensional plane on the basis of the characteristics of SH-waves, the ‘division-conjunction’ concept, the complex function, and moving-coordinate methods. The whole domain considered is divided into two subdomains, and the wave expressions are assumed in each subdomain. In the cylindrical subdomain, the wave function is constructed with the satisfaction of the zero-stress condition on the hill's surface automatically. In the other subdomain, the solution of the scattering waves is postulated under the stress-free condition on the horizontal surface. The analytical solutions of themodel established are obtained through a series of infinite linear algebraic equations, under the conditions that both the stress and displacement across the conjunction interface of the two subdomains are continuous. The numerical solutions are developed by truncating the infinite linear algebraic equations. The numerical simulations are performed for quantifying the displacements of the horizontal and semicylindrical hill surfaces subjected to incident SH waves, and the numerical results are verified with a comparison to the existing results of a case without subsurface hole.

Ground Motion of Two Scalene Triangle Hills and a Semi-Cylindrical Canyon under Incident SH-Waves

2011 ◽  
Vol 121-126 ◽  
pp. 862-866
Author(s):  
Zai Lin Yang ◽  
Hua Nan Xu
Keyword(s):  
Boundary Condition ◽  
Wave Function ◽  
Ground Motion ◽  
Complex Function ◽  
Polar Coordinates ◽  
Algebraic Equations ◽  
Sh Waves ◽  
Wave Fields ◽  
Numerical Examples ◽  
Scalene Triangle

The scattering of SH-waves by two scalene triangle hills and a semi-cylindrical canyon was surveyed here using the methods of wave function expansion, complex function and multi-polar coordinates. Based on “division”, we divided the analytical model into 3 parts, and constructed displacement solutions of wave fields that meet the boundary conditions in the three regions, respectively. The three domains were then conjoined to satisfy the “conjunction” condition to deduce a series of infinite algebraic equations about the problem combined with the boundary condition of semi-cylindrical canyon. Lastly, numerical examples were presented to investigate the influence of different parameters on the ground motion of the hills and the canyon.

Determination of crustal thickness from spectral behavior of SH waves

1969 ◽  
Vol 59 (3) ◽  
pp. 1247-1258
Author(s):  
Abou-Bakr K. Ibrahim
Keyword(s):  
Amplitude Spectrum ◽  
Body Waves ◽  
Multiple Reflections ◽  
Matrix Formulation ◽  
Sh Waves ◽  
Crustal Model ◽  
Amplitude Spectra ◽  
Phase Spectra ◽  
Zero Phase

abstract The amplitude spectrum obtained from Haskell's matrix formulation for body waves travelling through a horizontally layered crustal model shows a sequence of minima and maxima. It is known that multiple reflections within the crustal layers produce constructive and destructive interferences, which are shown as maxima and minima in the amplitude spectrum. Analysis of the minima in the amplitude spectra, which correspond to zero phase in the phase spectra, enables us to determine the thickness of the crust, provided the ratio of wave velocity in the crust to velocity under the Moho is known.

scholarly journals Dynamic Stress Analysis of a Circular-Lined Tunnel in Composite Strata-SH Wave Incidence

2020 ◽  
Vol 2020 ◽  
pp. 1-13
Author(s):  
Hui Qi ◽  
Yang Zhang ◽  
Jing Guo ◽  
Fuqing Chu ◽  
Mehmet Serkan Kirgiz
Keyword(s):  
Dynamic Stress ◽  
Complex Function ◽  
Sh Waves ◽  
Displacement Boundary ◽  
Dynamic Stress Concentration Factor ◽  
Finite Term ◽  
Scattering Wave ◽  
Seismic Wave Scattering ◽  
Dynamic Stress Analysis ◽  
Wave Incidence

It is necessary to study the problem of seismic wave scattering in composite stratum for tunnel engineering because the existence of composite strata will make the stress of tunnels more complicated during earthquakes. In this thesis, a series solution of the scattering wave field of the composite strata and lining is obtained using the complex function method. According to the stress and displacement boundary conditions between the composite stratum and the lining, a series of equations are established and are solved by means of Fourier transformation and finite term truncation, and the calculation errors are also discussed. Through programming calculations, the dynamic stress concentration factor (DSCF) of circular tunnels in the two types of composite strata, “hard-over-soft” and “soft-over-hard,” is analyzed when SH waves propagate, and certain conclusions on the scattering of SH waves that are distinguished from the case of single homogeneous layers are reached. The research in this article reveals some phenomena. For the Q345 steel lining in the calculation examples, it is found in this paper that increasing the thickness of the lining is effective to reduce the influence of the DSCF. But, for C30 concrete, increasing the thickness of the lining reduces the DSCF of the outer surface while increasing the DSCF of the inner surface.

Dynamic Response of Shallow Buried Tunnel Subjected to SH Wave

2010 ◽  
Vol 163-167 ◽  
pp. 4265-4268
Author(s):  
Zhi Gang Chen
Keyword(s):  
Stress Concentration ◽  
Half Space ◽  
Dynamic Stress ◽  
Complex Function ◽  
Least Square ◽  
Wave Number ◽  
Dynamic Stress Concentration ◽  
Algebraic Equations ◽  
Sh Wave ◽  
Scattering Wave

The dynamic stress concentration on quadratic and U-shaped cavities in half space, which are similar to the cross-section of the tunnels, is solved in this paper impacted by SH-wave. The analytical solution for the cavity in elastic half space is gained by the complex function method. In the complex plane, the scattering wave which satisfies the zero-stress condition at the horizontal surface can be constructed, the problem can be inverted into a set of algebraic equations to solve coefficients of the constructed scattering wave by least square method. For the earthquake-resistance researches, the numerical examples of the dynamic stress concentration around the quadratic and U-shaped cavities impacted by SH-wave are given. The influences of the dynamic stress concentration by the incident wave number and angle, the depth and shape of the cavity are discussed. It is showed that the interaction among the wave, the surface and the shallow buried tunnels should be cared in half space. In this situation, the dynamic stress concentration around the tunnel is greater obvious than the whole space.

scholarly journals Snow albedo sensitivity to macroscopic surface roughness using a new ray tracing model

2019 ◽  
Author(s):  
Fanny Larue ◽  
Ghislain Picard ◽  
Laurent Arnaud ◽  
Inès Ollivier ◽  
Clément Delcourt ◽  
...  
Keyword(s):  
Surface Roughness ◽  
Smooth Surface ◽  
Incident Angle ◽  
The Sun ◽  
Multiple Reflections ◽  
Snow Albedo ◽  
Snow Properties ◽  
Angle Effect ◽  
Effective Angle ◽  
The Impact

Abstract. Most models simulating snow albedo assume a flat and smooth surface, neglecting surface roughness. However, the presence of macroscopic roughness leads to a systematic decrease in albedo due to two effects: 1) photons are trapped in concavities (multiple reflection effect) and, 2) when the sun is low, the roughness sides facing the sun experience an overall decrease in the local incident angle relative to a smooth surface, promoting higher absorption, whilst the other sides has weak contributions because of the increased incident angle or because they are shadowed (called the effective angle effect here). This paper aims to quantify the impact of surface roughness on albedo and to assess the respective role of these two effects, with 1) observations over varying amounts of surface roughness, and 2) simulations using the new Rough Surface Ray Tracer (RSRT) model, based on a Monte Carlo method for photon transport calculation. The observations include spectral albedo (400–1050 nm) over manually-created roughness surfaces with multiple geometrical characteristics. Measurements highlight that even a low fraction of surface roughness features (7 % of the surface) causes an albedo decrease of 0.02 at 1000 nm when the solar zenith angle (Өs) is larger than 50°. For higher fractions (13 %, 27 % and 63 %), and when the roughness orientation is perpendicular to the sun, the decrease is of 0.03–0.04 at 700 nm and of 0.06–0.10 at 1000 nm. The impact is 20 % lower when roughness orientation is parallel to the sun. The observations are subsequently compared to RSRT simulations. Accounting for surface roughness improves the model observation agreement by a factor two at 700 nm and 1000 nm (errors of 0.03 and 0.04, respectively), compared to simulations considering a flat smooth surface. The model is used to explore the albedo sensitivity to surface roughness with varying snow properties and illumination conditions. Both multiple reflections and the effective angle effect have more impact with low SSA (

scholarly journals Photonic Stopband Filters Based on Graphene-Pair Arrays

2021 ◽  
Vol 11 (23) ◽  
pp. 11557
Author(s):  
Dong Zhao ◽  
Liyan Wang ◽  
Fangmei Liu ◽  
Dong Zhong ◽  
Min Wu
Keyword(s):  
Chemical Potential ◽  
Incident Angle ◽  
Graphene Sheets ◽  
Spatial Period ◽  
Compound System ◽  
Photonic Band Structure ◽  
Photonic Bandgaps ◽  
Bulk Substrate ◽  
Photonic Band ◽  
Incident Frequency

We investigate the photonic bandgaps in graphene-pair arrays. Graphene sheets are installed in a bulk substrate to form periodical graphene photonic crystal. The compound system approves a photonic band structure as a light impinges on it. Multiple stopbands are induced by changing the incident frequency of light. The stopbands widths and their central frequencies could be modulated through the graphene chemical potential. The number of stopbands decreases with the increase in the spatial period of graphene pairs. Otherwise, two full passbands are realized in the parameter space composed of the incident angle and the light frequency. This investigation has potentials applied in tunable multi-stopbands filters.

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