Deformation of a Flexible Disk Bonded to an Elastic Half Space—Application to the Lung

1980 ◽  
Vol 102 (3) ◽  
pp. 234-239 ◽  
Author(s):  
S. J. Lai-Fook ◽  
M. A. Hajji ◽  
T. A. Wilson
Keyword(s):  
Half Space ◽  
Poisson’S Ratio ◽  
Radial Strain ◽  
Lung Parenchyma ◽  
Elastic Half Space ◽  
Poisson's Ratio ◽  
Normal Displacement ◽  
Direct Estimate ◽  
Analytic Expressions ◽  
Flexible Disk

An analysis is presented of the deformation of a homogeneous, isotropic, elastic half space subjected to a constant radial strain in a circular area on the boundary. Explicit analytic expressions for the normal and radial displacements and the shear stress on the boundary are used to interpret experiments performed on inflated pig lungs. The boundary strain was induced by inflating or deflating the lung after bonding a flexible disk to the lung surface. The prediction that the surface bulges outward for positive boundary strain and inward for negative strain was observed in the experiments. Poisson’s ratio at two transpulmonary pressures was measured, by use of the normal displacement equation evaluated at the surface. A direct estimate of Poisson’s ratio was possible because the normal displacement of the surface depended uniquely on the compressibility of the material. Qualitative comparisons between theory and experiment support the use of continuum analyses in evaluating the behavior of the lung parenchyma when subjected to small local distortions.

The azimuthal and polar radiation patterns obtained from a horizontal stress applied at the surface of an elastic half space

1962 ◽  
Vol 52 (1) ◽  
pp. 27-36
Author(s):  
J. T. Cherry
Keyword(s):  
Surface Wave ◽  
Half Space ◽  
Rayleigh Waves ◽  
Poisson’S Ratio ◽  
Horizontal Stress ◽  
Elastic Half Space ◽  
The Body ◽  
Body Waves ◽  
Poisson's Ratio ◽  
A Value

Abstract The body waves and surface waves radiating from a horizontal stress applied at the free surface of an elastic half space are obtained. The SV wave suffers a phase shift of π at 45 degrees from the vertical. Also, a surface wave that is SH in character but travels with the Rayleigh velocity is shown to exist. This surface wave attenuates as r−3/2. For a value of Poisson's ratio of 0.25 or 0.33, the amplitude of the Rayleigh waves from a horizontal source should be smaller than the amplitude of the Rayleigh waves from a vertical source. The ratio of vertical to horizontal amplitude for the Rayleigh waves from the horizontal source is the same as the corresponding ratio for the vertical source for all values of Poisson's ratio.

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.

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.

Guided Surface Waves on an Elastic Half Space

1971 ◽  
Vol 38 (4) ◽  
pp. 899-905 ◽  
Author(s):  
L. B. Freund
Keyword(s):  
Wave Propagation ◽  
Surface Wave ◽  
Surface Waves ◽  
Half Space ◽  
Body Wave ◽  
Three Dimensional ◽  
Elastic Half Space ◽  
Normal Displacement ◽  
Rigid Barrier ◽  
Wave Disturbances

Three-dimensional wave propagation in an elastic half space is considered. The half space is traction free on half its boundary, while the remaining part of the boundary is free of shear traction and is constrained against normal displacement by a smooth, rigid barrier. A time-harmonic surface wave, traveling on the traction free part of the surface, is obliquely incident on the edge of the barrier. The amplitude and the phase of the resulting reflected surface wave are determined by means of Laplace transform methods and the Wiener-Hopf technique. Wave propagation in an elastic half space in contact with two rigid, smooth barriers is then considered. The barriers are arranged so that a strip on the surface of uniform width is traction free, which forms a wave guide for surface waves. Results of the surface wave reflection problem are then used to geometrically construct dispersion relations for the propagation of unattenuated guided surface waves in the guiding structure. The rate of decay of body wave disturbances, localized near the edges of the guide, is discussed.

Surface Settlement of a Deep Elastic Stratum Whose Modulus Increases Linearly with Depth

1972 ◽  
Vol 9 (4) ◽  
pp. 467-476 ◽  
Author(s):  
P. T. Brown ◽  
R. E. Gibson
Keyword(s):  
Half Space ◽  
Elastic Material ◽  
Poisson’S Ratio ◽  
Surface Displacement ◽  
Vertical Surface ◽  
Surface Settlement ◽  
Poisson's Ratio ◽  
Uniform Load ◽  
Circular Area ◽  
Wide Range

An examination has been made of the behavior of a half space of elastic material of constant Poisson's ratio, whose Young's modulus increases linearly with depth, and which is subject to a strip or circle of uniform load. Poisson's ratio was considered in the range zero to one-half, and the surface modulus ranged from zero to the value corresponding to a homogeneous material.Numerical values are presented for vertical surface displacement due to a load uniformly distributed over a circular area for Poisson's ratio = 1/2, 1/3 and 0, and for a wide range of inhomogeneity.

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.

Surface Displacement of a Convective Elastic Half-Space Under an Arbitrarily Distributed Fast-Moving Heat Source

1965 ◽  
Vol 87 (3) ◽  
pp. 729-734 ◽  
Author(s):  
F. F. Ling ◽  
V. C. Mow
Keyword(s):  
Heat Source ◽  
Half Space ◽  
Fast Moving ◽  
Constant Velocity ◽  
Surface Displacement ◽  
Elastic Half Space ◽  
Normal Displacement ◽  
Two Dimensional ◽  
Moving Heat Source ◽  
Thermoelasticity Theory

A solution of the normal displacement of the elastic half-space under an arbitrarily distributed fast-moving heat source of constant velocity within the two-dimensional quasi-static, uncoupled thermoelasticity theory is presented. The surface of the half-space is allowed to dissipate heat by convection. Moreover, an example associated with the problem of elastohydrodynamics is given.

Low Velocity Impact of an Elastic Plate Resting on Sand

1988 ◽  
Vol 55 (4) ◽  
pp. 887-894 ◽  
Author(s):  
H. L. Chen ◽  
W. Lin ◽  
L. M. Keer ◽  
S. P. Shah
Keyword(s):  
Half Space ◽  
Wave Speed ◽  
Impact Load ◽  
Radial Strain ◽  
Elastic Half Space ◽  
Low Velocity Impact ◽  
Target Plate ◽  
Low Velocity ◽  
Soil Response ◽  
Velocity Impact

This article describes the measurement and analysis of plate and soil response under low velocity impact. A free-drop impact system was developed to generate the dynamic loading on the plate free surface. The radial strain of the target plate, the longitudinal wave speed and the acceleration of the sand were measured. The measured wave speed data were then used to evaluate the elastic constants of the sand. An analysis based on linear elastodynamics was developed for transient waves on a thin plate resting on an elastic half space. The contact stresses and the normal displacements of the plate were taken as unknown functions. The contact between the plate and the half space were assumed frictionless. The experimental results of the radial strain at the bottom of the target plate and the acceleration of the sand beneath the center of the target plate were compared with the analytical solution. The arrival time, the duration, and the magnitude have good correlation between the analysis and experiment. The overall results appear good and provide an understanding of the transmission of impact load through the plate, the interaction between the plate and the sand, and the propagation of the load into the sand.

scholarly journals Internal Heat Source in Thermoelastic Microelongated Solid Under Green Lindsay Theory

2016 ◽  
Vol 46 (2) ◽  
pp. 65-82 ◽  
Author(s):  
Praveen Ailawalia ◽  
Sunil Kumar ◽  
Devinder Singh Pathania
Keyword(s):  
Heat Source ◽  
Half Space ◽  
Normal Force ◽  
Internal Heat ◽  
Internal Heat Source ◽  
Displacement Component ◽  
Elastic Half Space ◽  
Two Dimensional ◽  
Analytic Expressions ◽  
Gl Theory

Abstract The present study deals with two dimensional deformation, due to internal heat source in a thermoelastic microelongated solid. A mechanical force is applied along the interface of elastic half space and thermoelastic microelongated half space. The problem is in the context of Green Lindsay (GL) theory. The analytic expressions for displacement component, normal force stress, temperature distribution and microelongation have been derived. The effect of internal heat source and microelongation on the derived components have been depicted graphically.

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