A Numerical Simulation Approach to the Rayleigh Wave Particle Motion and the Poisson's Ratio of Mediums

2013 ◽  
Author(s):  
Wengfu Yu ◽  
Zhengping Liu
Keyword(s):  
Numerical Simulation ◽  
Rayleigh Wave ◽  
Particle Motion ◽  
Poisson’S Ratio ◽  
Poisson's Ratio ◽  
Simulation Approach

Some numerical solutions for Lamb's problem

1974 ◽  
Vol 64 (2) ◽  
pp. 473-491
Author(s):  
Harold M. Mooney
Keyword(s):  
Rayleigh Wave ◽  
Poisson’S Ratio ◽  
Pulse Width ◽  
Numerical Solutions ◽  
Pulse Height ◽  
P Wave ◽  
Poisson's Ratio ◽  
Wave Form ◽  
Lamb’S Problem ◽  
Wave Forms

abstract We consider a version of Lamb's Problem in which a vertical time-dependent point force acts on the surface of a uniform half-space. The resulting surface disturbance is computed as vertical and horizontal components of displacement, particle velocity, acceleration, and strain. The goal is to provide numerical solutions appropriate to a comparison with observed wave forms produced by impacts onto granite and onto soil. Solutions for step- and delta-function sources are not physically realistic but represent limiting cases. They show a clear P arrival (larger on horizontal than vertical components) and an obscure S arrival. The Rayleigh pulse includes a singularity at the theoretical arrival time. All of the energy buildup appears on the vertical components and all of the energy decay, on the horizontal components. The effects of Poisson's ratio upon vertical displacements for a step-function source are shown. For fixed shear velocity, an increase of Poisson's ratio produces a P pulse which is larger, faster, and more gradually emergent, an S pulse with more clear-cut beginning, and a much narrower Rayleigh pulse. For a source-time function given by cos2(πt/T), −T/2 ≦ T/2, a × 10 reduction in pulse width at fixed pulse height yields an increase in P and Rayleigh-wave amplitudes by factors of 1, 10, and 100 for displacement, velocity and strain, and acceleration, respectively. The observed wave forms appear somewhat oscillatory, with widths proportional to the source pulse width. The Rayleigh pulse appears as emergent positive on vertical components and as sharp negative on horizontal components. We show a theoretical seismic profile for granite, with source pulse width of 10 µsec and detectors at 10, 20, 30, 40, and 50 cm. Pulse amplitude decays as r−1 for P wave and r−12 for Rayleigh wave. Pulse width broadens slightly with distance but the wave form character remains essentially unchanged.

scholarly journals A single Rayleigh mode may exist with multiple values of phase-velocity at one frequency

2020 ◽  
Vol 222 (1) ◽  
pp. 582-594
Author(s):  
Thomas Forbriger ◽  
Lingli Gao ◽  
Peter Malischewsky ◽  
Matthias Ohrnberger ◽  
Yudi Pan
Keyword(s):  
Phase Velocity ◽  
Rayleigh Wave ◽  
Half Space ◽  
Wave Velocity ◽  
Poisson’S Ratio ◽  
P Wave ◽  
Poisson's Ratio ◽  
Wave Number ◽  
Homogeneous Layer ◽  
Rayleigh Mode

SUMMARY Other than commonly assumed in seismology, the phase velocity of Rayleigh waves is not necessarily a single-valued function of frequency. In fact, a single Rayleigh mode can exist with three different values of phase velocity at one frequency. We demonstrate this for the first higher mode on a realistic shallow seismic structure of a homogeneous layer of unconsolidated sediments on top of a half-space of solid rock (LOH). In the case of LOH a significant contrast to the half-space is required to produce the phenomenon. In a simpler structure of a homogeneous layer with fixed (rigid) bottom (LFB) the phenomenon exists for values of Poisson’s ratio between 0.19 and 0.5 and is most pronounced for P-wave velocity being three times S-wave velocity (Poisson’s ratio of 0.4375). A pavement-like structure (PAV) of two layers on top of a half-space produces the multivaluedness for the fundamental mode. Programs for the computation of synthetic dispersion curves are prone to trouble in such cases. Many of them use mode-follower algorithms which loose track of the dispersion curve and miss the multivalued section. We show results for well established programs. Their inability to properly handle these cases might be one reason why the phenomenon of multivaluedness went unnoticed in seismological Rayleigh wave research for so long. For the very same reason methods of dispersion analysis must fail if they imply wave number kl(ω) for the lth Rayleigh mode to be a single-valued function of frequency ω. This applies in particular to deconvolution methods like phase-matched filters. We demonstrate that a slant-stack analysis fails in the multivalued section, while a Fourier–Bessel transformation captures the complete Rayleigh-wave signal. Waves of finite bandwidth in the multivalued section propagate with positive group-velocity and negative phase-velocity. Their eigenfunctions appear conventional and contain no conspicuous feature.

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.

Influence of Refractory᾽s Poisson’s Ratio on the Stress Field of COREX Gasifier Top

2011 ◽  
Vol 418-420 ◽  
pp. 1686-1689
Author(s):  
Wen Dong Xue ◽  
Xiao Xiao Huang ◽  
Jing Xie ◽  
Qiang Ding
Keyword(s):  
Mechanical Properties ◽  
Numerical Simulation ◽  
Elastic Modulus ◽  
Stress Field ◽  
Time Use ◽  
Poisson’S Ratio ◽  
Poisson's Ratio ◽  
Resistance To Deformation ◽  
Long Time

Poisson’s ratio and elastic modulus are important parameters reflecting resistance to deformation and mechanical properties of refractory. In this paper the effect of posision’s ratio and elastic modulus on the stress field of the top of gasifier was investigated by numerical simulation. It is concluded that when for working lining poisson’s ratio is 0.15, elastic modulus is 128.8×107Pa, for permanent lining poisson's ratio is 0.1, the elastic modulus of 47.7 × 107Pa, the stress of the top is smaller and it is conductive to long-time use of top refractory.

Response of an Elastic Half Space to Expanding Surface Loads

1971 ◽  
Vol 38 (1) ◽  
pp. 99-110 ◽  
Author(s):  
D. C. Gakenheimer
Keyword(s):  
Rayleigh Wave ◽  
Exact Solutions ◽  
Half Space ◽  
Poisson’S Ratio ◽  
Elastic Half Space ◽  
Poisson's Ratio ◽  
Constant Rate ◽  
Different Depths ◽  
Surface Loads

A class of elastic half-space problems involving axisymmetric, normally applied, surface loads is investigated. Each load is assumed to suddenly emanate from a point on the surface and expand radially at a constant rate. The cases of loads shaped like a ring and a disk are considered in detail. Exact solutions are derived for the displacements at every point in the half space in terms of single integrals. Each integral is identified as a specific wave. The integrals are evaluated analytically and numerically for different depths in the half space, for loads expanding at superseismic, transeismic, and subseismic rates, and for different values of Poisson’s ratio. Moreover, the interaction of the loads and the Rayleigh wave is described. Then solutions are obtained for loads of other shapes by convoluting the ring and disk load solutions.

SONIC DETERMINATION OF THE ELASTIC PROPERTIES OF ICE

1947 ◽  
Vol 25a (2) ◽  
pp. 88-95 ◽  
Author(s):  
T. D. Northwood
Keyword(s):  
Rayleigh Wave ◽  
Young’S Modulus ◽  
Elastic Properties ◽  
Elastic Waves ◽  
Poisson’S Ratio ◽  
Young's Modulus ◽  
The Other ◽  
Poisson's Ratio ◽  
Wave Velocities

By measuring the velocity of various types of elastic waves in a solid it is possible to deduce Young's modulus and Poisson's ratio. Longitudinal, extensional, and Rayleigh wave velocities were measured in ice, the first by resonance in a rod and the other two by a pulsing technique. The value obtained for Young's modulus was 9.8 × 1010 dynes per cm.2 and for Poisson's ratio was 0.33.

On the determination of the polarization angle of the S wave

1962 ◽  
Vol 52 (1) ◽  
pp. 95-107
Author(s):  
Otto Nuttli ◽  
John D. Whitmore
Keyword(s):  
Wave Velocity ◽  
Particle Motion ◽  
Poisson’S Ratio ◽  
Epicentral Distance ◽  
Critical Distance ◽  
P Wave ◽  
Poisson's Ratio ◽  
Polarization Angle ◽  
Angle Of Incidence ◽  
S Wave

Abstract This study is concerned with determining the minimum epicentral distance for which it is permissible to obtain the value of the polarization angle of the S wave by measuring the angle between the great circle path at the station and the direction of the horizontal component of the S wave particle motion obtained from the seismograms. This critical distance can be determined by the fact that at smaller distances the particle motion of the earth's surface due to the incidence of S will be nonlinear (the SH and the horizontal and vertical components of SV will be out of phase with respect to one another) while at larger distances the particle motion will be linear. An analysis of the S motion recorded by the Galitzin-Wilip seismographs at Florissant indicates that the critical distance is 42 degrees. The periods of these S waves are of the order of 10 second. The analysis also shows that the effective P wave velocity of teleseismic waves at the earth's free surface is 7.74 km/sec, and the effective value of Poisson's ratio and the effective S wave velocity at the earth's surface are 0.25 and 4.46 km/sec, respectively. By effective values are meant the values of the velocities and Poisson's ratio that govern the angle of incidence of the waves at the earth's surface.

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