MULTI‐REFLECTED HEAD WAVES IN A SINGLE‐LAYERED MEDIUM

Geophysics ◽  
1966 ◽  
Vol 31 (5) ◽  
pp. 927-939 ◽  
Author(s):  
Yosio Nakamura
Keyword(s):  
Layered Medium ◽  
Fourier Transforms ◽  
Finite Thickness ◽  
Single Layer ◽  
Head Wave ◽  
Two Dimensional ◽  
Propagation Characteristics ◽  
Dimensional Model ◽  
Dispersive Effect ◽  
Head Waves

The propagation characteristics of surface‐reflected head waves have been studied experimentally using two‐ dimensional, Plexiglas‐aluminum and polystyrene‐aluminum, single‐layer models. In addition to the contributions from the reflected refractions (with reflections near the source) and the refracted reflections (with reflections near the receiver) those from the refraction‐reflection intermixtures (with reflections midway in the refraction path) have been found to be significant, resulting in a slight reinforcement of the surface‐reflected head waves with increasing distance. The phase relations of the arrivals have been examined by computing the Fourier transforms of the observed waveforms. It has been found that, relative to the principal head‐wave arrival, the surface‐reflected head waves exhibit an anomalous phase shift, which is due probably to the finite thickness of the model materials. For the dispersive effect to be negligible, the thickness of the two‐dimensional model must be less than approximately one‐fifteenth of the wavelength of interest.

Thermomechanical Behavior of Multilayered Media: Results

1990 ◽  
Vol 112 (2) ◽  
pp. 317-323 ◽  
Author(s):  
J. M. Leroy ◽  
A. Floquet ◽  
B. Villechaise
Keyword(s):  
Layered Medium ◽  
Finite Thickness ◽  
Thermomechanical Behavior ◽  
Stress Fields ◽  
Two Dimensional ◽  
Variable Properties ◽  
Dimensional Model ◽  
Multilayered Media ◽  
Thin Coatings ◽  
Two Dimensional Model

To study the thermoelastic behavior of coatings a two-dimensional model of a finite thickness layered medium submitted to a moving heat flux was presented in a previous paper (Leroy, Floquet, and Villechaise, 1989). The influence of thin coatings with variable properties or thicknesses on the temperature and stress fields is studied here. These results show that important stresses occur in a coating whose properties differ from those of the substrate, even for low temperature rises.

A STUDY OF TWO‐DIMENSIONAL HEAD WAVES IN FLUID AND SOLID SYSTEMS

Geophysics ◽  
1963 ◽  
Vol 28 (4) ◽  
pp. 563-581 ◽  
Author(s):  
John W. Dunkin
Keyword(s):  
Half Space ◽  
Vertical Displacement ◽  
Point Of View ◽  
Head Wave ◽  
Apparent Velocity ◽  
Two Dimensional ◽  
Multiple Reflections ◽  
Transient Wave ◽  
Line Load ◽  
Head Waves

The problem of transient wave propagation in a three‐layered, fluid or solid half‐plane is investigated with the point of view of determining the effect of refracting bed thickness on the character of the two‐dimensional head wave. The “ray‐theory” technique is used to obtain exact expressions for the vertical displacement at the surface caused by an impulsive line load. The impulsive solutions are convolved with a time function having the shape of one cycle of a sinusoid. The multiple reflections in the refracting bed are found to affect the head wave significantly. For thin refracting beds in the fluid half‐space the character of the head wave can be completely altered by the strong multiple reflections. In the solid half‐space the weaker multiple reflections affect both the rate of decay of the amplitude of the head wave with distance and the apparent velocity of the head wave by changing its shape. A comparison is made of the results for the solid half‐space with previously published results of model experiments.

scholarly journals Capillary-induced deformations of a thin elastic sheet

2016 ◽  
Vol 374 (2066) ◽  
pp. 20150169 ◽  
Author(s):  
N. D. Brubaker ◽  
J. Lega
Keyword(s):  
Finite Thickness ◽  
Three Dimensional ◽  
Two Dimensions ◽  
System Of Equations ◽  
Two Dimensional ◽  
Dimensional Model ◽  
Three Dimensional Model ◽  
Drop Volume ◽  
Exactly Solvable ◽  
Encapsulation Process

We develop a three-dimensional model for capillary origami systems in which a rectangular plate has finite thickness, is allowed to stretch and undergoes small deflections. This latter constraint limits our description of the encapsulation process to its initial folding phase. We first simplify the resulting system of equations to two dimensions by assuming that the plate has infinite aspect ratio, which allows us to compare our approach to known two-dimensional capillary origami models for inextensible plates. Moreover, as this two-dimensional model is exactly solvable, we give an expression for its solution in terms of its parameters. We then turn to the full three-dimensional model in the limit of small drop volume and provide numerical simulations showing how the plate and the drop deform due to the effect of capillary forces.

scholarly journals Frictionally Excited Thermoelastic Instability in Multi-Disk Clutches and Brakes

2000 ◽  
Vol 123 (4) ◽  
pp. 865-871 ◽  
Author(s):  
P. Decuzzi ◽  
M. Ciaverella ◽  
G. Monno
Keyword(s):  
Critical Speed ◽  
Finite Thickness ◽  
Thickness Ratio ◽  
Wave Parameter ◽  
Two Dimensional ◽  
Dimensional Model ◽  
Thermoelastic Instability ◽  
Dimensional Plane ◽  
Two Dimensional Model ◽  
Radial Thickness

The propensity toward thermoelastic instability (TEI) in multi-disk clutches and brakes is investigated by introducing a new bidimensional analytical model, where metal and friction disks are replaced by two-dimensional layers of finite thickness. This new model permits to estimate the effect of the thickness ratio a1/a2, between friction and metal disks, on the critical speed, critical wave parameter and migration speed of the sliding system. It is found that as the thickness ratio a1/a2 decreases the critical speed reduces significantly taking up values about 80 percent smaller than that predicted by previous two-dimensional models for commonly used ratios 0.1<a1/a2<1, whilst the critical wave parameter slightly increases. Therefore, not only the susceptibility towards TEI can be reduced by changing the material properties of the friction lining but also by adjusting suitably the thickness ratio of the disks. The two-dimensional model is also employed to determine the critical speed in a real multi-disk clutch, and the results are compared with a three-dimensional finite element code. It is shown that the critical speed estimated by the present two-dimensional plane strain model is in good agreement with that determined by the FE code for sufficiently large radial thickness of the disks, whilst the two-dimensional plane stress solution has to be used for relatively small radial thickness ratios. Also, it is found that the critical number of hot spots is independent of the radial thickness ratio and it is correctly predicted by the two-dimensional model.

scholarly journals SEISMIC MODEL STUDY OF REFRACTIONS FROM A LAYER OF FINITE THICKNESS

Geophysics ◽  
1954 ◽  
Vol 19 (3) ◽  
pp. 388-401 ◽  
Author(s):  
Frank Press ◽  
Jack Oliver ◽  
Maurice Ewing
Keyword(s):  
Travel Time ◽  
Layer Thickness ◽  
Finite Thickness ◽  
Selective Absorption ◽  
Two Dimensional ◽  
Seismic Model ◽  
Dimensional Model ◽  
Model Experiments ◽  
Model Study ◽  
Two Dimensional Model

Two dimensional model experiments on refractions from layers of finite thickness are described. Refractions can be unreliable for velocity and depth determinations when they occur with wavelengths which are large compared to the layer thickness. Discrepancies reported between refraction velocities and borehole velocities can be partially accounted for in this manner. Even simple two‐ and three‐layer models can show such effects as misleading second arrivals, echeloning of travel time curves, masked layers, and selective absorption in the overburden.

Synthetic seismograms in attenuating media

Geophysics ◽  
1983 ◽  
Vol 48 (12) ◽  
pp. 1575-1587 ◽  
Author(s):  
Thierry Bourbié ◽  
Alfonso Gonzalez‐Serrano
Keyword(s):  
Wave Theory ◽  
Relative Increase ◽  
Synthetic Seismograms ◽  
Head Wave ◽  
Complex Frequency ◽  
Two Dimensional ◽  
Borehole Data ◽  
Solid Interface ◽  
Working Space ◽  
Head Waves

Synthetic seismograms are computed in a two‐dimensional medium that contains contrasts both in the elastic and in the attenuation (Q) properties with depth. The case of a liquid‐solid interface, with and without a Q contrast between the two media, is examined in detail. We show the results when the S velocity in the solid is greater than the P velocity in the liquid. The synthetic seismograms show that the effect of the attenuation contrast is not noticeable on precritical reflections when the change in elastic properties is large even in the case of large Q contrast. When this situation occurs, there is a relative increase in the amplitude of the postcritical reflections and a decrease in amplitude of the head waves. It is interesting to notice that when two head waves are generated, the P head wave always has a very low amplitude with respect to the S head wave. This result agrees with what has been observed in borehole data. We also show the results obtained at a solid‐solid interface with and without Q contrast. The synthetic seismogram shows the same type of results as in the previous case but less pronounced due to the smaller portion of the total path occurring in attenuating media. It also shows that the converted waves (S — P and P — S) are of opposite polarities and so nearly cancel each other. The synthetic seismograms are calculated in the horizontal wavenumber‐frequency [Formula: see text] domain, and Fourier transformed back into offset‐time (x, t) domain. The choice of the [Formula: see text] domain as a working space is motivated by the fact that it allows us to include easily the effects of attenuation by specifying complex frequency‐dependent elastic moduli. The reflection and transmission coefficients in the ([Formula: see text], ω) domain are derived from a plane wave theory. Accurate geometric divergence is represented by using the exact Green’s functions in a two‐dimensional medium. The constant Q model for attenuation, derived by Kjartansson, is used.

HEAD WAVES FROM A BED OF FINITE THICKNESS

Geophysics ◽  
1962 ◽  
Vol 27 (6) ◽  
pp. 753-765 ◽  
Author(s):  
Franklyn K. Levin ◽  
John D. Ingram
Keyword(s):  
Layer Thickness ◽  
High Speed ◽  
Finite Thickness ◽  
Thin Layers ◽  
Head Wave ◽  
Amplitude Dependence ◽  
Head Waves ◽  
Zero Layer ◽  
Bar Velocity ◽  
Seismic Models

The behavior of the head wave from a high‐speed layer embedded in a low‐speed half‐space has been investigated with two‐dimensional seismic models. Twelve layer thicknesses ranging from four wavelengths to one‐tenth wavelength were used. A simple theory based on interference between the head wave and the reflections from the bottom of the layer gave amplitude‐distance values which agreed with the observations for layer thicknesses down to about one‐third of a wavelength. For thick layers, the experimental amplitude dependence on distance was different from the theoretical law (−3/2 power of the distance). The velocity minimum for thin layers discovered by Lavergne was confirmed and a possible slight velocity maximum at intermediate layer thicknesses noted. The velocity for zero layer thickness appeared to be greater than the free bar velocity. Systematic variations of head‐wave spectra with layer thickness occurred.

Thermomechanical Behavior of Multilayered Media: Theory

1989 ◽  
Vol 111 (3) ◽  
pp. 538-544 ◽  
Author(s):  
J. M. Leroy ◽  
A. Floquet ◽  
B. Villechaise
Keyword(s):  
Layered Medium ◽  
Fourier Transforms ◽  
Finite Thickness ◽  
Thermoelastic Stress ◽  
Media Theory ◽  
Hard Coatings ◽  
Stress Fields ◽  
Multilayered Media ◽  
Wide Range ◽  
Heavy Loads

Hard coatings are more and more used to improve the mechanical and tribological behavior of surfaces. Thermomechanical cracking can occur in these coatings when they slide under heavy loads. We present a two-dimensional model of a finite thickness layered medium submitted to a moving heat source. The analytical solution of the temperature and thermoelastic stress fields is obtained using Fourier transforms. The behavior of each layer is described by transfer-matrices and a relation between the displacement- and stress-vectors is given. The originality of the study is the use of a Fast Fourier Transform algorithm. With this method, calculation time is reduced, no singularity problems are met in the inverse transform and each parameter (especially the thickness of the layers) can be studied over a wide range.

Commitment to pro- versus counter-attitudinal behavior and the dynamics of social representations

2002 ◽  
Vol 61 (1) ◽  
pp. 34-44 ◽  
Author(s):  
Eric Tafani ◽  
Lionel Souchet
Keyword(s):  
Higher Education ◽  
Social Representations ◽  
Cognitive Restructuring ◽  
Social Representation ◽  
Two Dimensional ◽  
Dimensional Model ◽  
Social Actions ◽  
The Social ◽  
Two Dimensional Model ◽  
Students Attitudes

This research uses the counter-attitudinal essay paradigm ( Janis & King, 1954 ) to test the effects of social actions on social representations. Thus, students wrote either a pro- or a counter-attitudinal essay on Higher Education. Three forms of counter-attitudinal essays were manipulated countering respectively a) students’ attitudes towards higher education; b) peripheral beliefs or c) central beliefs associated with this representation object. After writing the essay, students expressed their attitudes towards higher education and evaluated different beliefs associated with it. The structural status of these beliefs was also assessed by a “calling into question” test ( Flament, 1994a ). Results show that behavior challenging either an attitude or peripheral beliefs induces a rationalization process, giving rise to minor modifications of the representational field. These modifications are only on the social evaluative dimension of the social representation. On the other hand, when the behavior challenges central beliefs, the same rationalization process induces a cognitive restructuring of the representational field, i.e., a structural change in the representation. These results and their implications for the experimental study of representational dynamics are discussed with regard to the two-dimensional model of social representations ( Moliner, 1994 ) and rationalization theory ( Beauvois & Joule, 1996 ).

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