Scattering of Compressional Waves by a Rigid Spheroidal Inclusion

1973 ◽  
Vol 40 (4) ◽  
pp. 1073-1077 ◽  
Author(s):  
Michael A. Oien ◽  
Yih-Hsing Pao
Keyword(s):  
Dynamic Stress ◽  
Translational Motion ◽  
Expansion Method ◽  
Compressional Wave ◽  
Low Frequencies ◽  
Compressional Waves ◽  
Spheroidal Inclusion ◽  
Eigenfunction Expansion Method ◽  
Concentration Factors ◽  
Stress Concentration Factors

The scattering of an axial plane harmonic compressional wave by a mobile rigid spheroidal inclusion in an elastic medium is investigated. A solution valid for low frequencies is obtained using the eigenfunction expansion method. Numerical results are presented for the excited translational motion of the spheroid and for dynamic stress-concentration factors.

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.

A theory of compressional wave attenuation in noncohesive sediments

Geophysics ◽  
1985 ◽  
Vol 50 (8) ◽  
pp. 1311-1317 ◽  
Author(s):  
C. McCann ◽  
D. M. McCann
Keyword(s):  
Wave Attenuation ◽  
Compressional Wave ◽  
Solid Particles ◽  
Biot’S Theory ◽  
Attenuation Coefficients ◽  
Low Frequencies ◽  
Biot's Theory ◽  
Compressional Waves ◽  
High Frequencies ◽  
Water Saturated

Published reviews indicate that attenuation coefficients of compressional waves in noncohesive, water‐saturated sediments vary linearly with frequency. Biot’s theory, which accounts for attenuation in terms of the viscous interaction between the solid particles and pore fluid, predicts in its presently published form variation proportional to [Formula: see text] at low frequencies and [Formula: see text] at high frequencies. A modification of Biot’s theory which incorporates a distribution of pore sizes is presented and shown to give excellent agreement with new and published attenuation data in the frequency range 10 kHz to 2.25 MHz. In particular, a linear variation of attenuation with frequency is predicted in that range.

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.

Transient stress concentration at an elliptical discontinuity

1969 ◽  
Vol 4 (4) ◽  
pp. 261-266 ◽  
Author(s):  
W G James ◽  
W P T North
Keyword(s):  
Stress Concentration ◽  
Dynamic Stress ◽  
Stress Wave Propagation ◽  
Transient Stress ◽  
Simplifying Assumptions ◽  
Concentration Factors ◽  
Stress Concentration Factors ◽  
The One ◽  
Two Parameters ◽  
Laser Light Source

In this investigation, the photoelastic technique with a modulated-ruby-laser light source was used to determine the maximum dynamic-stress concentration factors in a strut containing a symmetrically located elliptical discontinuity. The two parameters, time after impact and size of discontinuity, were considered. Some simplifying assumptions and the one- and two-dimensional theory of stress-wave propagation were used to develop a theoretical solution which agrees well with experimental results.

Diffraction of Plane Compressional Waves by an Array of Nanosized Cylindrical Holes

2010 ◽  
Vol 78 (2) ◽  
Author(s):  
Q. F. Zhang ◽  
G. F. Wang ◽  
P. Schiavone
Keyword(s):  
Surface Energy ◽  
Dynamic Stress ◽  
Surface Elasticity ◽  
Expansion Method ◽  
Stress Concentrations ◽  
Compressional Waves ◽  
Circular Holes ◽  
Cylindrical Holes ◽  
Effect Of Surface ◽  
Dynamic Stress Concentrations

When the radius of a hole reduces to nanometers, the influence of surface energy becomes prominent in its mechanical behavior. In the present paper, we consider the diffraction of plane compressional waves by an array of nanosized circular holes in an elastic medium. The effect of surface energy is taken into account through surface elasticity theory. Using the wave expansion method, we derive the corresponding elastic diffraction fields. Dynamic stress concentrations around the holes and the scattering cross section are calculated to address the surface effects on the diffraction phenomena.

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.

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.

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