The Influence of the Curvature of Spherical Waves on Dynamic Stress Concentration

1967 ◽  
Vol 34 (2) ◽  
pp. 373-379 ◽  
Author(s):  
F. C. Moon ◽  
Y-H. Pao
Keyword(s):  
Stress Concentration ◽  
Dynamic Stress ◽  
Plane Waves ◽  
Spherical Wave ◽  
Elastic Solid ◽  
Incident Wavelength ◽  
Dynamic Stresses ◽  
Low Frequencies ◽  
Compressional Waves ◽  
Spherical Waves

From a study of scattering of spherical compressional waves by a spherical cavity in an elastic solid, the dynamic stresses on the surface of the cavity are computed and compared with those due to plane compressional waves. At low frequencies, stresses due to spherical waves, even with a very small curvature, are higher than the corresponding ones for plane waves. Only when the incident wavelength is shorter than the distance between the source and the cavity can a spherical wave be approximated by a plane wave.

scholarly journals Plane Waves Scattered by a Spherical Inclusion in a Half Space of Poroelastic Material

2020 ◽  
Vol 03 (02) ◽  
pp. 1-1
Author(s):  
Doo-Sung Lee ◽  
Keyword(s):  
Half Space ◽  
Existence And Uniqueness ◽  
Spherical Inclusion ◽  
Plane Waves ◽  
Spherical Wave ◽  
Wave Functions ◽  
Successive Approximations ◽  
Compressional Waves ◽  
Poroelastic Material ◽  
The Given

This paper concerns a poroelastic half-space in which plane compressional waves are scattered by a spherical inclusion. Addition theorems for the spherical wave functions are utilized to meet the boundary conditions on the plane, and the satisfaction of the given conditions on the boundary of the sphere leads to three infinite series equations, whose solution can be acquired by successive approximations. Further, its existence and uniqueness are discussed.

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.

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.

On Dynamic Stress Concentration Around a Discontinuity

1967 ◽  
Vol 34 (2) ◽  
pp. 385-391
Author(s):  
S. L. Cheng ◽  
A. Jahanshahi
Keyword(s):  
Stress Concentration ◽  
Elastic Plate ◽  
Dynamic Stress ◽  
Source Location ◽  
Dynamic Stress Concentration ◽  
Dynamic Stresses ◽  
Time Harmonic ◽  
Line Force ◽  
Finite Distance ◽  
Rigid Insert

The redistribution of dynamic stresses due to the presence of a circular cylindrical discontinuity in an unbounded isotropic homogeneous elastic plate is studied. The source of excitation is a time-harmonic line force located at a finite distance from the discontinuity. In particular, the effects of source location on the concentration of energy around a rigid insert or a cavity is explored.

scholarly journals A Green’s Function for Acoustic Problems in Pekeris Waveguide Using a Rigorous Image Source Method

2021 ◽  
Vol 11 (6) ◽  
pp. 2722
Author(s):  
Zhiwen Qian ◽  
Dejiang Shang ◽  
Yuan Hu ◽  
Xinyang Xu ◽  
Haihan Zhao ◽  
...  
Keyword(s):  
Green’S Function ◽  
Shallow Water ◽  
Green's Function ◽  
Plane Waves ◽  
Spherical Wave ◽  
Sound Field ◽  
Efficient Computation ◽  
Image Source ◽  
Source Method ◽  
Pekeris Waveguide

The Green’s function (GF) directly eases the efficient computation for acoustic radiation problems in shallow water with the use of the Helmholtz integral equation. The difficulty in solving the GF in shallow water lies in the need to consider the boundary effects. In this paper, a rigorous theoretical model of interactions between the spherical wave and the liquid boundary is established by Fourier transform. The accurate and adaptive GF for the acoustic problems in the Pekeris waveguide with lossy seabed is derived, which is based on the image source method (ISM) and wave acoustics. First, the spherical wave is decomposed into plane waves in different incident angles. Second, each plane wave is multiplied by the corresponding reflection coefficient to obtain the reflected sound field, and the field is superposed to obtain the reflected sound field of the spherical wave. Then, the sound field of all image sources and the physical source are summed to obtain the GF in the Pekeris waveguide. The results computed by this method are compared with the standard wavenumber integration method, which verifies the accuracy of the GF for the near- and far-field acoustic problems. The influence of seabed attenuation on modal interference patterns is analyzed.

Dynamic stress concentration around a hole in a viscoelastic plate

1995 ◽  
Vol 111 (1-2) ◽  
pp. 1-12 ◽  
Author(s):  
H. G. Georgiadis ◽  
A. P. Rigatos ◽  
N. C. Charalambakis
Keyword(s):  
Stress Concentration ◽  
Dynamic Stress ◽  
Viscoelastic Plate ◽  
Dynamic Stress Concentration

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.

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