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.

scholarly journals Dynamic Stress and Displacement in an Elastic Half-Space with a Cylindrical Cavity

2011 ◽  
Vol 18 (6) ◽  
pp. 827-838 ◽  
Author(s):  
İ. Coşkun ◽  
H. Engin ◽  
A. Özmutlu
Keyword(s):  
Free Surface ◽  
Boundary Conditions ◽  
Half Space ◽  
Cylindrical Cavity ◽  
Circular Cross Section ◽  
Elastic Half Space ◽  
Least Square ◽  
Polar Coordinates ◽  
Wave Number ◽  
Forcing Function

The dynamic response of an elastic half-space with a cylindrical cavity in a circular cross-section is analyzed. The cavity is assumed to be infinitely long, lying parallel to the plane-free surface of the medium at a finite depth and subjected to a uniformly distributed harmonic pressure at the inner surface. The problem considered is one of plain strain, in which it is assumed that the geometry and material properties of the medium and the forcing function are constant along the axis of the cavity. The equations of motion are reduced to two wave equations in polar coordinates with the use of Helmholtz potentials. The method of wave function expansion is used to construct the displacement fields in terms of the potentials. The boundary conditions at the surface of the cavity are satisfied exactly, and they are satisfied approximately at the free surface of the half-space. Thus, the unknown coefficients in the expansions are obtained from the treatment of boundary conditions using a collocation least-square scheme. Numerical results, which are presented in the figures, show that the wave number (i.e., the frequency) and depth of the cavity significantly affect the displacement and stress.

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.

Effects of Surface Energy on Scattering of SH Waves by an Elastic Half-Plane with a Semi-Cylindrical Cavity

2012 ◽  
Vol 627 ◽  
pp. 698-704
Author(s):  
Zhi Ying Ou ◽  
Xiao Wei Liu ◽  
Qiong Deng
Keyword(s):  
Surface Energy ◽  
Cylindrical Cavity ◽  
Dynamic Stress ◽  
Shear Waves ◽  
Surface Elasticity ◽  
Expansion Method ◽  
Stress Fields ◽  
Sh Waves ◽  
Wave Function Expansion Method ◽  
Incident Waves

When the radius of materials and structral devices reduces to nanometers, the influence of surface energy becomes prominent in its mechanical behavior. In the frame of surface elasticity, the scattering of anti-plan shear waves by an elastic half-plan with a semi-cylindrical cavity considered the surface energy are investigated in this paper. When the boundary condition at the straight edge of the half-plan is traction free, the analytical solutions of stress fields of the half plan with semi-culindrical cavity are expressed by employing a wave function expansion method. The results show that surface energy has a significant effect on the scattering of anti-plan shear waves as the radius of the semi-cylindrical cavity shrinks to nanoscale. The effects of incident waves with different frequencies and incident angel, radius of semi-cylindrical cavity and surface energy on the dynamic stress concentration around the semi-cylindrical cavity are discussed in detail.

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.

The Dynamic Response of Elastic Half Space Including a Semi-Lining Hill

2013 ◽  
Vol 753-755 ◽  
pp. 1712-1718
Author(s):  
Jing Fu Nan
Keyword(s):  
Dynamic Response ◽  
Half Space ◽  
Line Source ◽  
Complex Function ◽  
Arbitrary Point ◽  
Elastic Half Space ◽  
Displacement Function ◽  
Algebraic Equations ◽  
Out Of Plane ◽  
Horizontal Interface

The dynamic response of elastic half space including semi-cylindrical lining hill while bearing out-of-plane harmonic line source loading on horizontal interface is investigated using the method of complex function and Greens function. the displacement function of incidence wave is given while a out-of-plane harmonic line source is loaded on arbitrary point of horizontal interface;and the solution domain is divided into two domains, an elastic half space with the semi-circular canyon and a cylindrical lining; the scattering wave of semi-cylindrical canyon and the standing wave of cylindrical lining are constructed. Finally, it conjoins the two domains, and a series of infinite algebraic equations can be obtained to settle this problem. In the end, the numerical expressions of the ground motion in the horizontal surface are discussed.

scholarly journals Dynamic Response of a Circular Tunnel in an Elastic Half Space

2017 ◽  
Vol 2017 ◽  
pp. 1-12 ◽  
Author(s):  
İrfan Coşkun ◽  
Demirhan Dolmaseven
Keyword(s):  
Boundary Conditions ◽  
Half Space ◽  
Dynamic Pressure ◽  
Equations Of Motion ◽  
Surrounding Medium ◽  
Elastic Half Space ◽  
Polar Coordinates ◽  
Wave Number ◽  
Circular Tunnel ◽  
Tunnel Wall

The vibration of a circular tunnel in an elastic half space subjected to uniformly distributed dynamic pressure at the inner boundary is studied in this paper. For comparison purposes, two different ground materials (soft and hard soil) are considered for the half space. Under the assumption of plane strain, the equations of motion for the tunnel and the surrounding medium are reduced to two wave equations in polar coordinates using Helmholtz potentials. The method of wave expansion is used to construct the displacement fields in terms of displacement potentials. The boundary conditions associated with the problem are satisfied exactly at the inner surface of the tunnel and at the interface between the tunnel and surrounding medium, and they are satisfied approximately at the free surface of the half space. A least-squares technique is used for satisfying the stress-free boundary conditions at the half space. It is shown by comparison that the stresses and displacements are significantly influenced by the properties of the surrounding soil, wave number (i.e., the frequency), depth of embedment, and thickness of the tunnel wall.

SH-wave velocity in a fiber-reinforced anisotropic layer overlying a gravitational heterogeneous half-space

2015 ◽  
Vol 11 (3) ◽  
pp. 386-400 ◽  
Author(s):  
Rajneesh Kakar
Keyword(s):  
Dispersion Equation ◽  
Half Space ◽  
Love Wave ◽  
Elastic Half Space ◽  
Wave Number ◽  
Fiber Reinforced ◽  
Sh Wave ◽  
Dimensionless Wave Number ◽  
Sh Waves ◽  
Content Type

Purpose – The purpose of this paper is to investigate the existence of SH-waves in fiber-reinforced layer placed over a heterogeneous elastic half-space. Design/methodology/approach – The heterogeneity of the elastic half-space is caused by the exponential variations of density and rigidity. As a special case when both the layers are homogeneous, the derived equation is in agreement with the general equation of Love wave. Findings – Numerically, it is observed that the velocity of SH-waves decreases with the increase of heterogeneity and reinforced parameters. The dimensionless phase velocity of SH-waves increases with the decreases of dimensionless wave number and shown through figures. Originality/value – In this work, SH-wave in a fiber-reinforced anisotropic medium overlying a heterogeneous gravitational half-space has been investigated analytically and numerically. The dispersion equation for the propagation of SH-waves has been observed in terms of Whittaker function and its derivative of second degree order. It has been observed that on the removal of heterogeneity of half-space, and reinforced parameters of the layer, the derived dispersion equation reduces to Love wave dispersion equation thereby validates the solution of the problem. The equation of propagation of Love wave in fiber-reinforced medium over a heterogeneous half-space given by relevant authors is also reduced from the obtained dispersion relation under the considered geometry.

The Scattering of SH-Wave Caused by Subsurface Circular Cavities in a Layered Half-Space

2011 ◽  
Vol 488-489 ◽  
pp. 226-229
Author(s):  
Dong Ni Chen ◽  
Hui Qi ◽  
Yong Shi
Keyword(s):  
Half Space ◽  
Elastic Layer ◽  
Complex Function ◽  
Expansion Method ◽  
Elastic Half Space ◽  
Wave Functions ◽  
Large Radius ◽  
Algebraic Equations ◽  
Sh Wave ◽  
Linear Algebraic Equations

The scattering of SH-wave caused by the subsurface circular cavities in an elastic half-space covered with an elastic layer was discussed, which was based on the complex function method ,wave functions expansion method and big circular arc postulation method in which the circular boundary of large radius was used to approximate straight boundary of surface elastic layer. By the theory of Helmholtz, the general solution of the Biot’s wave function was achieved. Utilizing the complex series expansion technology and the boundary conditions, we could transform the present problem into the problem in which we needed to solve the infinite linear algebraic equations with unknown coefficients in wave functions. Finally, the dynamic stress concentration factors around the circular cavities were discussed in numerical examples.

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.

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