Scattering of SH waves around circular canyon in inhomogeneous wedge space

SUMMARY Scattering of SH waves around a circular canyon in radial inhomogeneous wedge space is investigated in this paper. Based on the complex function method, the governing equation with variable coefficients is transformed into a standard Helmholtz equation and the corresponding analytical solution to this problem is derived. The unknown coefficients in the wavefield is obtained by enforcing the stress-free condition in the circular canyon, then the incident, reflected and scattering waves in the total wavefield are all acquired. Through the calculation and analysis of the parameters that affect the ground motion, the influence of the circular canyon on the ground motion in the radial inhomogeneous wedge space is obtained. Moreover, combined with graphical results, the effects by inhomogeneous parameter on ground motion with circular canyon in wedge space are conspicuous.

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The Interaction of a Cylindrical Elastic Inclusion with Semicircular Disconnected Curve and Linear Cracks in an Homogeneous Medium by SH-Waves

Key Engineering Materials ◽

10.4028/www.scientific.net/kem.348-349.357 ◽

2007 ◽

Vol 348-349 ◽

pp. 357-360

Author(s):

Qi Hui ◽

Jia Xi Zhao

Keyword(s):

Green’S Function ◽

Half Space ◽

Green's Function ◽

Function Method ◽

Dynamic Stress ◽

Elastic Inclusion ◽

Complex Function ◽

Dynamic Stress Intensity Factor ◽

Homogeneous Medium ◽

Sh Waves

The scattering of SH waves by a cylindrical elastic inclusion with a semicircular disconnected curve and linear cracks in an homogeneous medium is investigated and the solution of dynamic stress intensity factor is given by Green’s function, complex function method. Firstly, we can divide the space into up-and-down parts along the X axis. In the lower half space, a new suitable Green’s function for the present problem is constructed.In the upper half space, the Green’s function has been given by reference [5]. Thereby the semicircular disconnected curve can be constructed when the two parts are bonded along the interface and the linear cracks can be constructed using the method of crack-division and the integral equations can be obtained by the use of continuity conditions at the X axis. Finally, some examples and results of dynamic stress intensify factor are given and the influence of the parameters is discussed.

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An analysis of highly viscous flow using Imai's complex function method with application to screen printing (Fluid Dyn. Res. 10, 11)

Fluid Dynamics Research ◽

10.1016/0169-5983(93)90043-a ◽

1993 ◽

Vol 11 (4) ◽

pp. 183

Author(s):

J Kawabata ◽

H Shi-igai ◽

K Yabuno ◽

T Saito

Keyword(s):

Viscous Flow ◽

Function Method ◽

Screen Printing ◽

Complex Function ◽

Complex Function Method

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A Method for Stress Intensity Factor Calculation of Typical MSD Configurations

Advanced Materials Research ◽

10.4028/www.scientific.net/amr.700.149 ◽

2013 ◽

Vol 700 ◽

pp. 149-152 ◽

Cited By ~ 2

Author(s):

Jin Fang Zhao ◽

Qun Zhao

Keyword(s):

Stress Intensity Factor ◽

Stress Intensity ◽

Intensity Factor ◽

Function Method ◽

Complex Function ◽

Calculation Process ◽

Complex Function Method

This paper introduced compounding method to calculate the SIF of typical MSD configurations. Complex function method was proposed to calculate the modification coefficient of the adjacent holes. Combining the method with compounding method, the SIF calculation of typical MSD configurations was achieved. The calculation process is easy to operate and the results are reliable which can be verified by FEM calculation. By studying the SIF results of typical MSD configurations, a series of conclusions with practical value in engineering can be obtained.

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A complex function method of SH wave scattering in inhomogeneous medium

Acta Mechanica ◽

10.1007/s00707-017-1876-6 ◽

2017 ◽

Vol 228 (10) ◽

pp. 3469-3481 ◽

Cited By ~ 2

Author(s):

Zai-lin Yang ◽

Chong-qun Zhang ◽

Guan-xi-xi Jiang ◽

Pei-lei Yan ◽

Yong Yang

Keyword(s):

Inhomogeneous Medium ◽

Wave Scattering ◽

Function Method ◽

Complex Function ◽

Sh Wave ◽

Complex Function Method

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The Complex Function Method Roadway Section Design of the Soft Coal Seam

Mathematical Problems in Engineering ◽

10.1155/2016/9291412 ◽

2016 ◽

Vol 2016 ◽

pp. 1-12

Author(s):

Shihao Tu ◽

Zhaoxin Li ◽

Zhiwei Ye ◽

Cun Zhang ◽

Lei Zhang

Keyword(s):

Coal Seam ◽

Function Method ◽

Vertical Wall ◽

Complex Function ◽

Surrounding Rock ◽

Type Steel ◽

Soft Coal ◽

Distribution Laws ◽

Soft Coal Seam ◽

Complex Function Method

As for the sophisticated advanced support technique of vertical wall semicircle arch roadway in the three-soft coal seam, a design of flat top U-shape roadway section was put forward. Based on the complex function method, the surrounding rock displacement and stress distribution laws both of vertical wall semicircle arch roadway and of flat top U-shape roadway were obtained. The results showed that the displacement distribution laws in the edge of roadway surrounding rock were similar between the two different roadways and the area of plasticity proportion of flat top U-shape roadway approximately equals that of vertical wall semicircle arch roadway. Based on finite element method, the bearing behaviors of the U-type steel support under the interaction of surrounding rock in vertical wall semicircle arch roadway and flat top U-shape roadway were analyzed. The results showed that, from a mechanics perspective, U-type steel support can fulfill the requirement of surrounding rock supporting in flat top U-shape roadway and vertical wall semicircle arch roadway. The field measurement of mining roadway surrounding rock displacement in Zouzhuang coal mine working face 3204 verified the accuracy of theoretical analysis and numerical simulation.

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

Applied Mechanics and Materials ◽

10.4028/www.scientific.net/amm.121-126.862 ◽

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.

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