A numerical study of the Rayleigh wave particle motions excited by a point source and Poisson's ratio for lateral inhomogeneous half-spaces

2015 ◽  
Vol 123 ◽  
pp. 242-255 ◽  
Author(s):  
Wenfu Yu ◽  
Zhengping Liu
Keyword(s):  
Point Source ◽  
Rayleigh Wave ◽  
Poisson’S Ratio ◽  
Numerical Study ◽  
Poisson's Ratio

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 Numerical Study of the Screening Effectiveness of Open Trenches for High-Speed Train-Induced Vibration

2014 ◽  
Vol 2014 ◽  
pp. 1-11 ◽  
Author(s):  
Chih-hung Chiang ◽  
Pei-hsun Tsai
Keyword(s):  
Poisson’S Ratio ◽  
High Speed ◽  
Numerical Study ◽  
Cutoff Frequency ◽  
Poisson's Ratio ◽  
High Speed Train ◽  
High Speed Rail ◽  
Train Speed ◽  
Open Trench ◽  
Screening Effectiveness

This study used the 2D boundary element method in time domain to examine the screening effectiveness of open trenches on reducing vibration generated by a high-speed train. The parameters included configurations of the trench, train speed, the distance between the source and the trench, and the Poisson’s ratio of the soil. A reducing displacement level (in dB scale) was defined and used to evaluate the screening effectiveness of a wave barrier. The maximal reducing displacement level reached 25 dB when an open trench was used as a wave barrier. The depth of an open trench is a main influential parameter of screening effectiveness. The cutoff frequency of the displacement spectrum increases with decreasing trench depth. The maximal screening effectiveness occurs when the depth is 0.3-0.4 Rayleigh wavelength. Using an open trench as a wave barrier can reduce 10–25 dB of vibration amplitude at frequencies between 30 and 70 Hz. A considerable increase in screening effectiveness of the open trench was observed from 30 to 70 Hz, which matches the main frequencies of vibration induced by Taiwan High Speed Rail. The influence of trench width on screening effectiveness is nonsignificant except for frequencies from 30 to 40 Hz. Poisson’s ratio has various effects on the reduction of vibration at frequencies higher than 30 Hz.

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.

Numerical Study on Axial Crushing of Auxetic Foam-Filled Square Tube

2020 ◽  
Vol 975 ◽  
pp. 159-164
Author(s):  
Saeid Mohsenizadeh ◽  
Zaini Ahmad ◽  
Amran Alias
Keyword(s):  
Energy Absorption ◽  
Poisson’S Ratio ◽  
Numerical Study ◽  
Progressive Collapse ◽  
Poisson's Ratio ◽  
Foam Core ◽  
Negative Poisson’S Ratio ◽  
Negative Poisson's Ratio ◽  
Absorption Performance ◽  
Foam Filled

Filling the thin-walled tubes with a foam core is a typical method to enhance the energy absorption performance and stabilize their crushing responses under impact loading. Recently, auxetic foam material with negative Poisson’s ratio has gained remarkable popularity as an effective candidate to enhance the energy absorption capability of structures. In this paper, polyurethane auxetic foam is suggested as a foam core with the negative Poisson’s ratio of-0.31. Numerical simulation was performed to quantify the crush characteristics of auxetic foam-filled square aluminum tubes for variations in initial width of tube under quasi-static axial loading using the nonlinear finite element (FE) code LS-Dyna. Based on the numerical results, the influence of tube width was quantified in terms of energy absorption (EA), specific energy absorption (SEA), initial peak force (Pmax) and crush force efficiency (CFE). It is found that the progressive collapse and deformation modes of auxetic foam-filled tube (AFFT) is pronouncedly affected by varying the tube width. Furthermore, the SEA of AFFT is remarkably sensitive to the tube width variations, yet show low sensitivity to the EA of AFFT. The present study provides new design information on the crush response and energy absorption performance of auxetic foam-filled square tube with varying tube width.

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