Dynamic Stresses Concentrations of SH Wave by Circular Tunnel with Lining

2011 ◽  
Vol 323 ◽  
pp. 18-22 ◽  
Author(s):  
Yi Guang Zhang ◽  
Chuan Lu Zhou ◽  
Yi Xian Liu
Keyword(s):  
Stress Concentration ◽  
Dynamic Stress ◽  
Wave Number ◽  
Dynamic Stress Concentration ◽  
Sh Wave ◽  
Circular Tunnel ◽  
Dynamic Stresses ◽  
Shear Elasticity ◽  
Concentration Factors ◽  
Stress Concentration Factors

Based on the scattering theory of elastic waves, employing the wave function expansion method, the scattering and the dynamic stresses concentration of SH wave by circular tunnel with lining are investigated. The analytical solution of the problem is derived, and the numerical solution of the dynamic stress concentration factors around the lining is presented. The effects of the shear elasticity of the surrounding rock and the lining, the wave number on the dynamic stress concentration factors are analyzed. Analysis has shown that the shear elasticity of the surrounding rock and the wave number are factors that influence dynamic stress concentration factor, and provide important theoretical foundation for the earthquake evaluation of lining.

On the Effects of Source Proximity on the Dynamic Stresses Around a Cylindrical Cavity

1967 ◽  
Vol 34 (2) ◽  
pp. 359-364 ◽  
Author(s):  
M. T. Jakub ◽  
C. C. Mow
Keyword(s):  
Stress Concentration ◽  
Plane Wave ◽  
Cylindrical Cavity ◽  
Dynamic Stress ◽  
Poisson Ratio ◽  
Cylindrical Wave ◽  
Wave Number ◽  
Dynamic Stress Concentration ◽  
Concentration Factors ◽  
Stress Concentration Factors

Analysis of the interaction of a cylindrical wave impinging on a cylindrical cavity is presented. It is assumed that a line source is located an arbitrary distance from the cavity and that its strength varies harmonically in time. The resulting dynamic stress concentration factors at the cavity wall are determined by considering the wave-diffraction effects. Numerical results indicate that the dynamic stress concentration factors around the cavity are dependent upon (a) distance from the source to the cavity, (b) wave number, and (c) the Poisson ratio of the medium. At high wave number (high frequency), the response to an incident cylindrical wave becomes almost identical with the response to an incident plane wave. At low wave number, however, the response departs drastically from all previous investigations where the incident wave was assumed to be a plane wave. Stress concentration factors substantially higher than those determined in earlier studies were noted in the present analysis.

Dynamic Antiplane Interaction of Subsurface Circular Cavities in a Semi-Infinite Piezoelectric Medium

2009 ◽  
Author(s):  
Tianshu Song ◽  
Tamman Merhej ◽  
Qingna Shang ◽  
Dong Li
Keyword(s):  
Stress Concentration ◽  
Dynamic Stress ◽  
Numerical Solutions ◽  
Piezoelectric Medium ◽  
Dynamic Stress Concentration ◽  
Characteristic Parameters ◽  
Time Harmonic ◽  
Concentration Factors ◽  
Stress Concentration Factors ◽  
Piezoelectric Characteristic

In the present work, dynamic interaction is investigated theoretically between several circular cavities near the surface in a semi-infinite piezoelectric medium subjected to time-harmonic incident anti-plane shearing. The analyses are based upon the use of complex variable and multi coordinates. Dynamic stress concentration factors at the edges of the subsurface circular cavities are obtained by solving boundary value problems with the method of orthogonal function expansion. Some numerical solutions about two interacting subsurface circular cavities in a semi-infinite piezoelectric medium are plotted so as to show how the frequencies of incident wave, the piezoelectric characteristic parameters of the material and the structural geometries influence on the dynamic stress concentration factors.

Dynamic Anti-Plane Behaviors of Interacting Circular Cavities in an Infinite Piezoelectric Medium

2008 ◽  
Author(s):  
Tianshu Song ◽  
Dong Li ◽  
Lili Sun
Keyword(s):  
Stress Concentration ◽  
Dynamic Stress ◽  
Piezoelectric Medium ◽  
Dynamic Stress Concentration ◽  
Wave Load ◽  
Plane Shear ◽  
Time Harmonic ◽  
Concentration Factors ◽  
Stress Concentration Factors ◽  
Piezoelectric Characteristic

In this article, dynamic interaction is investigated theoretically between several circular cavities in an infinite piezoelectric medium under time-harmonic incident anti-plane shear wave load. The theoretical formulations are based upon the use of complex variable and multi-coordinates. Dynamic stress concentration factors at the edges of the circular cavities are obtained by solving boundary value problems with the method of orthogonal function expansion. As examples, some calculating results of two interacting circular cavities in an infinite piezoelectric medium are plotted to show how the frequencies of incident wave, the piezoelectric characteristic parameters of the material and the structural geometries influence on the dynamic stress concentration factors.

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 Surface Effects on the Scattering of SH-Wave Around an Arbitrary Shaped Nano-Cavity

2019 ◽  
Vol 2019 ◽  
pp. 1-9
Author(s):  
Hongmei Wu ◽  
Zhiying Ou
Keyword(s):  
Stress Concentration ◽  
Dynamic Stress ◽  
Numerical Solutions ◽  
Surface Effects ◽  
Numerical Results ◽  
Wave Number ◽  
Dynamic Stress Concentration ◽  
Sh Wave ◽  
Special Cases ◽  
Variable Function

By using the complex variable function theory and the conformal mapping method, the scattering of plane shear wave (SH-wave) around an arbitrary shaped nano-cavity is studied. Surface effects at the nanoscale are explained based on the surface elasticity theory. According to the generalized Yong–Laplace equations, the boundary conditions are given, and the infinite algebraic equations for solving the unknown coefficients of the scattered wave solutions are established. The numerical solutions of the stress field can be obtained by using the orthogonality of trigonometric functions. Lastly, the numerical results of dynamic stress concentration factor around a circular hole, an elliptic hole and a square hole as the special cases are discussed. The numerical results show that the surface effect and wave number have a significant effect on the dynamic stress concentration, and prove that our results from theoretical derivation are correct.

scholarly journals Dynamic analysis of a cylindrical cavity in inhomogeneous elastic half-space subjected to SH waves

2017 ◽  
Vol 24 (1) ◽  
pp. 299-311 ◽  
Author(s):  
Zailin Yang ◽  
Guanxixi Jiang ◽  
Haiyi Tang ◽  
Baitao Sun ◽  
Yong Yang
Keyword(s):  
Stress Concentration ◽  
Helmholtz Equation ◽  
Half Space ◽  
Cylindrical Cavity ◽  
Variable Coefficient ◽  
Dynamic Stress ◽  
Dynamic Stress Concentration ◽  
Mapping Technique ◽  
Concentration Factors ◽  
Stress Concentration Factors

Based on complex function methods and a multipolar coordinate system, the scattering induced by a cylindrical cavity in a radially inhomogeneous half-space is investigated. Mass density of the half-space varies depending on the distance from the centre of the cavity while the shear modulus is always constant. The wave velocity is expressed as a function of radius vector and the Helmholtz equation is a partial differential equation with a variable coefficient. By means of a conformal mapping technique, the Helmholtz equation with a variable coefficient is transferred into its normal form. Then, displacement fields and corresponding stress components are deduced. Applying the boundary conditions, dynamic stress concentration factors around the cavity are obtained and analyzed. Typical numerical results are presented to demonstrate the distribution of dynamic stress concentration factors when influencing parameters are assumed.

Dynamic Stress Concentration on a Semi-Infinite Piezoelectric Medium With a Circular Cavity Near the Surface

2007 ◽  
Author(s):  
Tianshu Song ◽  
Shilong Wang
Keyword(s):  
Stress Concentration ◽  
Dynamic Stress ◽  
Piezoelectric Medium ◽  
Dynamic Stress Concentration ◽  
Circular Cavity ◽  
Characteristic Parameters ◽  
Time Harmonic ◽  
Concentration Factors ◽  
Stress Concentration Factors ◽  
Piezoelectric Characteristic

Dynamic interaction is investigated theoretically between a circular cavity and the surface in a semi-infinite piezoelectric medium subjected to time-harmonic incident anti-plane shearing in the present paper. The formulations are based on the method of complex variable and wave function expandedness. Dynamic stress concentration factors at the edge of the circular cavity are obtained by solving boundary value problems with the method of orthogonal function expansion. The calculating results are plotted so as to show how the frequencies of incident wave, the piezoelectric characteristic parameters of the material and the structural geometries influence upon the dynamic stress concentration factors.

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