Effect of an elastically restrained boundary on SV-wave radiation patterns

1968 ◽  
Vol 58 (2) ◽  
pp. 497-520
Author(s):  
Y. T. Huang
Keyword(s):  
Boundary Condition ◽  
Wave Propagation ◽  
Free Boundary ◽  
Boundary Conditions ◽  
Elastic Wave ◽  
Solid Earth ◽  
Elastic Constants ◽  
Wave Radiation ◽  
Free Boundary Conditions ◽  
Elastically Restrained

Abstract In the solution of elastic wave propagation equations applied to solid earth, it is customarily assumed that free boundary conditions are satisfied at a surface which is in contact with the atmosphere. Situations which depart from this boundary condition have now been studied for arbitrary combinations of the Lamé elastic constants. The solutions are given for a homogeneous, isotropic half space.

An optimal absorbing boundary condition for elastic wave modeling

Geophysics ◽  
1995 ◽  
Vol 60 (1) ◽  
pp. 296-301 ◽  
Author(s):  
Chengbin Peng ◽  
M. Nafi Toksöz
Keyword(s):  
Boundary Condition ◽  
Wave Propagation ◽  
Finite Difference ◽  
Boundary Conditions ◽  
Elastic Wave ◽  
Short Note ◽  
Absorbing Boundary Conditions ◽  
Parallel Computer ◽  
Absorbing Boundary Condition ◽  
Absorbing Boundary

Absorbing boundary conditions are widely used in numerical modeling of wave propagation in unbounded media to reduce reflections from artificial boundaries (Lindman, 1975; Clayton and Engquist, 1977; Reynolds, 1978; Liao et al., 1984; Cerjan et al., 1985; Randall, 1988; Higdon, 1991). We are interested in a particular absorbing boundary condition that has maximum absorbing ability with a minimum amount of computation and storage. This is practical for 3-D simulation of elastic wave propagation by a finite‐difference method. Peng and Toksöz (1994) developed a method to design a class of optimal absorbing boundary conditions for a given operator length. In this short note, we give a brief introduction to this technique, and we compare the optimal absorbing boundary conditions against those by Reynolds (1978) and Higdon (1991) using examples of 3-D elastic finite‐difference modeling on an nCUBE-2 parallel computer. In the Appendix, we also give explicit formulas for computing coefficients of the optimal absorbing boundary conditions.

The Effect of Wave Propagation on Seismic Response at Transmitting Boundary of Discrete System

2018 ◽  
Vol 878 ◽  
pp. 110-114
Author(s):  
Sang Hun Lee ◽  
Takao Endo ◽  
Ryutaro Kawana
Keyword(s):  
Wave Propagation ◽  
Free Boundary ◽  
Boundary Conditions ◽  
Seismic Response ◽  
Ground Motion ◽  
Response Analysis ◽  
Free Boundaries ◽  
Propagation Condition ◽  
Free Boundary Conditions ◽  
Transmitting Boundary

When analyzing the seismic response of a very long elevated structure such as a Shinkansen viaduct, it is common practice to analyze a cutout of the structure under consideration and treat its both ends as free boundaries. This is attributable to the assumption that seismic response analysis assuming free boundary conditions is more conservative than one assuming non-free boundary conditions. In this study, after finding out that response to harmonic ground motion can be greater than under free-boundary conditions if outward energy dissipation occurs from the analysis domain, a series of numerical experiments was performed to determine whether such phenomena occur in seismic response. Then, after confirming that the frequency components of ground motion that satisfy the wave propagation condition greatly affect seismic response, the study showed that the area of the wave propagation condition region of the Fourier spectrum can be used as an indicator by which to judge the likelihood of occurrence of such phenomena.

On the Wave Propagation in an Elastic Hollow Cylinder With Long-Range Cohesion Forces

1986 ◽  
Vol 53 (1) ◽  
pp. 121-124
Author(s):  
J. L. Nowinski
Keyword(s):  
Wave Propagation ◽  
Free Boundary ◽  
Boundary Conditions ◽  
Long Range ◽  
Fourier Transforms ◽  
Frequency Equation ◽  
Considerable Decrease ◽  
Free Boundary Conditions ◽  
Short Waves ◽  
Stress Components

After a brief derivation of the formula for the nonlocal moduli, Fourier transforms of the stress components in their nonlocal aspect are established. Satisfaction of the traction-free boundary conditions leads to the frequency equation of the problem. A particular case involving longitudinal Lame´ modes is analyzed in more detail. A numerical example solved shows a considerable decrease of the speed and the frequency of the short waves as compared with those of long waves studied in the classical theory.

scholarly journals Local Well-Posedness for Free Boundary Problem of Viscous Incompressible Magnetohydrodynamics

Mathematics ◽  
2021 ◽  
Vol 9 (5) ◽  
pp. 461
Author(s):  
Kenta Oishi ◽  
Yoshihiro Shibata
Keyword(s):  
Free Surface ◽  
Free Boundary ◽  
Boundary Conditions ◽  
Stokes Equations ◽  
Mhd Flow ◽  
Transmission Conditions ◽  
Well Posedness ◽  
Anisotropic Space ◽  
Free Boundary Conditions ◽  
Incompressible Magnetohydrodynamics

In this paper, we consider the motion of incompressible magnetohydrodynamics (MHD) with resistivity in a domain bounded by a free surface. An electromagnetic field generated by some currents in an external domain keeps an MHD flow in a bounded domain. On the free surface, free boundary conditions for MHD flow and transmission conditions for electromagnetic fields are imposed. We proved the local well-posedness in the general setting of domains from a mathematical point of view. The solutions are obtained in an anisotropic space Hp1((0,T),Hq1)∩Lp((0,T),Hq3) for the velocity field and in an anisotropic space Hp1((0,T),Lq)∩Lp((0,T),Hq2) for the magnetic fields with 2<p<∞, N<q<∞ and 2/p+N/q<1. To prove our main result, we used the Lp-Lq maximal regularity theorem for the Stokes equations with free boundary conditions and for the magnetic field equations with transmission conditions, which have been obtained by Frolova and the second author.

scholarly journals Identification of Corrosion on a Hollow Tube Using Vibration

2014 ◽  
Vol 564 ◽  
pp. 176-181
Author(s):  
S.T. Cheng ◽  
Nawal Aswan Abdul Jalil ◽  
Zamir A. Zulkefli
Keyword(s):  
Free Boundary ◽  
Boundary Conditions ◽  
Natural Frequency ◽  
Impact Loading ◽  
Structural Damage ◽  
Natural Frequencies ◽  
Localized Corrosion ◽  
Free Boundary Conditions ◽  
The Impact ◽  
Impact Vibration

Vibration based technique have so far been focused on the identification of structural damage. However, not many studies have been conducted on the corrosion identification on pipes. The objective of this paper is to identify corrosion on pipes from vibration measurements. A hollow pipe, 500 mm in length with 63.5 mm in diameter was subjected to impact loading using an impact hammer to identify the natural frequency of the tube in two conditions i) without any corrosion and ii) with an induced localized 40 mm by 40 mm corrosion at the middle of the pipe. The shift of natural frequencies of the structures under free boundary conditions was examined for each node of excitation. The results showed that there is a shift in natural frequency of the pipe, between 3 and 4 Hz near to the corrosion area. It can suggested that that the impact vibration is capable of identifying of localized corrosion on a hollow tube.

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