Scattering of Love Waves by a Surface-Breaking Crack

1986 ◽  
Vol 53 (3) ◽  
pp. 587-592 ◽  
Author(s):  
Y. C. Angel
Keyword(s):  
Integral Equation ◽  
Fourier Transform ◽  
Love Wave ◽  
Mixed Boundary ◽  
Wave Mode ◽  
Love Waves ◽  
Reflection Coefficients ◽  
Mixed Boundary Value Problem ◽  
Displacement Fields ◽  
Surface Breaking Crack

The interaction of Love waves with a surface-breaking crack normal to the free surface is investigated. By the use of Fourier transform techniques, the mixed-boundary value problem is reduced to a singular integral equation which is solved numerically. It is shown that the reflected and transmitted displacement fields at some distance from the crack are the superposition of a finite number of Love-wave modes. The reflection coefficients for the first three modes and the transmission coefficient are plotted versus the frequency. Several sharp resonances are observed. Each resonance corresponds to the vanishing of the amplitude of a particular Love-wave mode.

scholarly journals Electrostatic potential calculation by application of walk-on-spheres method

2018 ◽  
pp. 152-160
Author(s):  
Liudmila Vladimirova ◽  
Irina Rubtsova ◽  
Nikolai Edamenko
Keyword(s):  
Integral Equation ◽  
Problem Solving ◽  
Boundary Value Problem ◽  
Mixed Boundary ◽  
Boundary Value ◽  
Mixed Boundary Value Problem ◽  
Equation Solving ◽  
Electrostatic Potential Calculation ◽  
Walk On Spheres Algorithm ◽  
Boundary Form

The paper is devoted to mixed boundary-value problem solving for Laplace equation with the use of walk-on-spheres algorithm. The problem under study is reduced to finding a solution of integral equation with the kernel nonzero only at some sphere in the domain considered. Ulam-Neumann scheme is applied for integral equation solving; the appropriate Markov chain is introduced. The required solution value at a certain point of the domain is approximated by the expected value of special statistics defined on Markov paths. The algorithm presented guarantees the average Markov trajectory length to be finite and allows one to take into account boundary conditions on required solution derivative and to avoid Markov paths ending in the neighborhood of the boundaries where solution values are not given. The method is applied for calculation of electric potential in the injector of linear accelerator. The purpose of the work is to verify the applicability and effectiveness of walk-on-spheres method for mixed boundary-value problem solving with complicated boundary form and thus to demonstrate the suitability of Monte Carlo methods for electromagnetic fields simulation in beam forming systems. The numerical experiments performed confirm the simplicity and convenience of this method application for the problem considered.

Vibratory Motion of a Body on an Elastic Half Plane

1968 ◽  
Vol 35 (4) ◽  
pp. 697-705 ◽  
Author(s):  
P. Karasudhi ◽  
L. M. Keer ◽  
S. L. Lee
Keyword(s):  
Integral Equation ◽  
Half Plane ◽  
Good Accuracy ◽  
Coupling Effect ◽  
Mixed Boundary ◽  
Mixed Boundary Value Problem ◽  
Dual Integral Equations ◽  
Entire Surface ◽  
Vibratory Motion ◽  
Rocking Vibration

The vertical, horizontal and rocking vibrations of a body on the surface of an otherwise unloaded half plane are studied. The problems are formulated so that one stress vanishes over the entire surface, and an oscillating displacement is prescribed in the loaded region. The problems are mixed with respect to the prescribed displacement and the remaining stress. Each case leads to a mixed boundary value problem represented by dual integral equations which are reduced to a single Fredholm integral equation. Although numerical methods are used to solve the integral equation, the contact stresses are found to be presentable in closed form to good accuracy. An estimate of the stiffnesses for coupled horizontal and rocking vibration is also suggested and it is found that the coupling effect is significant.

Adhesive Contact Between the Surface Wave and a Rigid Strip

1995 ◽  
Vol 62 (2) ◽  
pp. 368-372 ◽  
Author(s):  
O. Y. Zharii
Keyword(s):  
Integral Equation ◽  
Surface Wave ◽  
Stress Distribution ◽  
Contact Area ◽  
Mixed Boundary ◽  
Closed Form Solution ◽  
Adhesive Contact ◽  
Form Solution ◽  
Mixed Boundary Value Problem ◽  
Analysis Of Variation

A problem of adhesive contact between the running surface wave and a rigid strip is investigated. The mixed boundary-value problem of elastodynamics is reduced to a singular integral equation for a complex combination of stresses and an exact closed-form solution of it has been derived. Analysis of variation of contact area dimensions, stress distribution and rotor velocity on the frequency of excitation displayed significant differences between the results corresponding to conditions of adhesion and slipping in contact area. The origin of these differences is discussed.

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