Transmission of Rayleigh wave through a surface crack in elastic half-space

2011 ◽  
Author(s):  
Marina G. Zhuchkova ◽  
Daniil P. Kouzov
Keyword(s):  
Rayleigh Wave ◽  
Half Space ◽  
Surface Crack ◽  
Elastic Half Space

Rayleigh-type surface wave on a rotating orthotropic elastic half-space with impedance boundary conditions

2020 ◽  
Vol 26 (21-22) ◽  
pp. 1980-1987
Author(s):  
Baljeet Singh ◽  
Baljinder Kaur
Keyword(s):  
Surface Wave ◽  
Boundary Conditions ◽  
Rayleigh Wave ◽  
Surface Waves ◽  
Half Space ◽  
Rotation Rate ◽  
Secular Equation ◽  
Elastic Half Space ◽  
Impedance Boundary ◽  
Impedance Boundary Conditions

The propagation of Rayleigh type surface waves in a rotating elastic half-space of orthotropic type is studied under impedance boundary conditions. The secular equation is obtained explicitly using traditional methodology. A program in MATLAB software is developed to obtain the numerical values of the nondimensional speed of Rayleigh wave. The speed of Rayleigh wave is illustrated graphically against rotation rate, nondimensional material constants, and impedance boundary parameters.

Impedance of Strip-Traveling Waves on an Elastic Half Space: Asymptotic Solution

1974 ◽  
Vol 41 (2) ◽  
pp. 412-416
Author(s):  
S. H. Crandall ◽  
A. K. Nigam
Keyword(s):  
Asymptotic Solution ◽  
Rayleigh Wave ◽  
Half Space ◽  
Traveling Wave ◽  
Load Distribution ◽  
Wave Speed ◽  
Elastic Half Space ◽  
Surface Load ◽  
Shear Wave Speed ◽  
Rayleigh Wave Speed

The dynamic normal-load distribution across a strip that is required to maintain a plane progressive wave along its length is studied for the case where the strip is of infinite length and lies on the surface of a homogeneous isotropic elastic half space. This configuration is proposed as a preliminary idealized model for analyzing the dynamic interaction between soils and flexible foundations. The surface load distribution across the strip and the motion of the strip are related by a pair of dual integral equations. An asymptotic solution is obtained for the limiting case of small wavelength. The nature of this solution depends importantly on the propagation velocity of the strip-traveling wave in comparison with the Rayleigh wave speed, the shear wave speed and the dilatational wave speed. When the strip-traveling wave propagates faster than the Rayleigh wave speed, a pattern of trailing Rayleigh waves is shed from the strip. The limiting amplitude of the trailing waves is provided by the asymptotic solution.

scholarly journals Approximate formula for the H/V ratio of Rayleigh waves in incompressible orthotropic half-spaces coated by a thin elastic layer

2017 ◽  
Vol 39 (4) ◽  
pp. 365-374
Author(s):  
Pham Chi Vinh ◽  
Tran Thanh Tuan ◽  
Le Thi Hue
Keyword(s):  
Free Surface ◽  
Rayleigh Wave ◽  
Half Space ◽  
Rayleigh Waves ◽  
Elastic Layer ◽  
Approximate Formula ◽  
Elastic Half Space ◽  
Displacement Amplitude ◽  
Vertical Displacements ◽  
Thin Elastic Layer

This paper is concerned with the propagation of Rayleigh waves in an incompressible orthotropic elastic half-space coated with a thin incompressible orthotropic elastic layer. The main purpose of the paper is to establish an approximate formula for the Rayleigh wave H/V ratio (the ratio between the amplitudes of the horizontal and vertical displacements of Rayleigh waves at the traction-free surface of the layer). First, the relations between the traction amplitude vector and the displacement amplitude vector of Rayleigh waves at two sides of the interface between the layer and the half-space are created using the Stroh formalism and the effective boundary condition method. Then, an approximate formula for the Rayleigh wave H/V ratio of third-order in terms of dimensionless thickness of the layer has been derived by using these relations along with the Taylor expansion of the displacement amplitude vector of the thin layer at its traction-free surface. It is shown numerically that the obtained formula is a good approximate one. It can be used for extracting mechanical properties of thin films from measured values of the  Rayleigh wave H/V ratio.

A New Formula for the Rayleigh Wave Velocity

2012 ◽  
Vol 452-453 ◽  
pp. 233-237
Author(s):  
Xue Feng Liu ◽  
You Hua Fan
Keyword(s):  
Rayleigh Wave ◽  
Half Space ◽  
Wave Velocity ◽  
Complex Number ◽  
Computer Time ◽  
Elastic Half Space ◽  
S Wave ◽  
Rayleigh Wave Velocity ◽  
New Formula

The formula for the Rayleigh wave velocity in isotropic elastic half-space is studied by many researchers. In their deductions, Cardan’s formula of cubic equations is often used. Based on another formula instead of Cardan’s formula, a new formula for the Rayleigh wave velocity that does not contain complex number is presented here. Our new formula is more reasonable as both the parameters and Rayleigh wave velocity are real. And the computer time can be reduced since there is no complex computation. With this new formula, the variation of Rayleigh wave velocity with the parameters is computed. It shows that Rayleigh wave velocity decreases with the increase of Poission’s ratio when S-wave velocity is fixed.

Scattering of a pulsed Rayleigh wave by a spherical cavity in an elastic half space

Wave Motion ◽  
1983 ◽  
Vol 5 (2) ◽  
pp. 137-143 ◽  
Author(s):  
Anders Boström ◽  
Gerhard Kristensson
Keyword(s):  
Rayleigh Wave ◽  
Half Space ◽  
Spherical Cavity ◽  
Elastic Half Space

RAYLEIGH‐WAVE MOTION IN AN ELASTIC HALF‐SPACE

Geophysics ◽  
1965 ◽  
Vol 30 (1) ◽  
pp. 97-101 ◽  
Author(s):  
W. A. Sorge
Keyword(s):  
Rayleigh Wave ◽  
Half Space ◽  
Rayleigh Waves ◽  
Wave Motion ◽  
Elastic Half Space ◽  
Two Dimensional ◽  
Seismic Model

Measurements made on Rayleigh waves below the surface of a simulated elastic half‐space confirm in detail the behavior predicted by theory. These measurements, made by means of a two‐dimensional seismic model, show that the amplitude of the Rayleigh wave falls off rapidly with increasing depth.

Vibration Attenuation Characters in Deep Holes under Road Traffic Load

2013 ◽  
Vol 353-356 ◽  
pp. 761-767
Author(s):  
Zheng Jun Mei
Keyword(s):  
Rayleigh Wave ◽  
Half Space ◽  
Road Traffic ◽  
Attenuation Factor ◽  
Horizontal Displacement ◽  
Peak Frequency ◽  
Elastic Half Space ◽  
Traffic Load ◽  
Vibration Measurement ◽  
Attenuation Law

Through the field vibration measurement of 50m and 80m deep holes under road traffic load, the attenuation law of displacement in holes with depth under traffic and traffic-free conditions was discussed in the time and frequency domains. Some conclusions were drawn as follows: RMS attenuation factor was close to 0.2 and the displacement is obviously reduced at a depth of about 40m; the peak frequency decreased as the depth gradually increased. Compared with the attenuation law in elastic half-space Rayleigh wave, it was found that the horizontal displacement reduced more slowly than the elastic half-space Rayleigh wave and the attenuation factor was gradually close to the attenuation curve of the elastic half-space Rayleigh wave with the increase of the depth; the attenuation factor of the vertical displacement gradually reduced as the depth increased and reduced much faster than elastic half-space Rayleigh wave.

The attenuation of a Rayleigh wave in a half-space by a surface impedance

1966 ◽  
Vol 62 (4) ◽  
pp. 811-827 ◽  
Author(s):  
R. D. Gregory
Keyword(s):  
Surface Wave ◽  
Rayleigh Wave ◽  
Half Space ◽  
Logarithmic Singularity ◽  
Elastic Half Space ◽  
Body Waves ◽  
Impedance Boundary Condition ◽  
Impedance Boundary ◽  
Elastic Potentials ◽  
Time Harmonic

AbstractA time harmonic Rayleigh wave, propagating in an elastic half-space y ≥ 0, is incident on a certain impedance boundary condition on y = 0, x > 0. The resulting field consists of a reflected surface wave, scattered body waves, and a transmitted surface wave appropriate to the new boundary conditions. The elastic potentials are found exactly by Fourier transform and the Wiener-Hopf technique in the case of a slightly dissipative medium. The ψ potential is found to have a logarithmic singularity at (0,0), but the φ potential though singular is bounded there. Analytic forms are given for the amplitudes of the reflected and transmitted surface waves, and for the scattered field. The reflexion coefficient is found to have a simple form for small impedances. A uniqueness theorem, based on energy considerations, is proved.

THE REFLECTION OF RAYLEIGH WAVES BY A HIGH IMPEDANCE OBSTACLE ON A HALF‐SPACE

Geophysics ◽  
1960 ◽  
Vol 25 (6) ◽  
pp. 1195-1202 ◽  
Author(s):  
R. W. Fredricks ◽  
L. Knopoff
Keyword(s):  
Reflection Coefficient ◽  
Rayleigh Wave ◽  
Half Space ◽  
Poisson’S Ratio ◽  
Vertical Displacement ◽  
Elastic Half Space ◽  
Poisson's Ratio ◽  
Dual Integral Equations ◽  
High Impedance ◽  
Theoretic Solution

The reflection of a time‐harmonic Rayleigh wave by a high impedance obstacle in shearless contact with an elastic half‐space of lower impedance is examined theoretically. The potentials are found by a function—theoretic solution to dual integral equations. From these potentials, a “reflection coefficient” is defined for the surface vertical displacement in the Rayleigh wave. Results show that the reflected wave is π/2 radians out of phase with the incident wave for arbitrary Poisson’s ratio. The modulus of the “reflection coefficient” depends upon Poisson’s ratio, and is evaluated as [Formula: see text] for σ=0.25.

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