Dynamic Stresses and Displacements Around Cylindrical Discontinuities Due to Plane Harmonic Shear Waves

1963 ◽  
Vol 30 (4) ◽  
pp. 598-604 ◽  
Author(s):  
C. C. Mow ◽  
L. J. Mente
Keyword(s):  
Rigid Body ◽  
Incident Wave ◽  
Rigid Inclusion ◽  
Poisson’S Ratio ◽  
Density Ratio ◽  
Body Motion ◽  
Poisson's Ratio ◽  
Wave Number ◽  
Plane Shear ◽  
Dynamic Stresses

The problem of dynamic stresses and displacements around a cavity and rigid inclusion of arbitrary density is examined for an elastic medium during the passage of a plane shear wave. In the cavity case, the dynamic stresses and displacements are found to be dependent upon the incident wave number and Poisson’s ratio of the medium. In the rigid-inclusion case it is found that dynamic stresses and the rigid-body rotation and translation are dependent upon the incident wave numbers, the Poisson’s ratio, and the density ratio of the medium and the insert. Close coupling is observed between the stresses and the rigid-body motion of the insert.

A study of the inconsistent observations in the fault-plane project

1958 ◽  
Vol 48 (1) ◽  
pp. 17-31
Author(s):  
J. H. Hodgson ◽  
W. M. Adams
Keyword(s):  
Poisson’S Ratio ◽  
Significant Variation ◽  
Fault Plane ◽  
Epicentral Distance ◽  
Density Ratio ◽  
Poisson's Ratio ◽  
Final Conclusion ◽  
The Core

Abstract The 65 solutions published in the fault-plane project of the Dominion Observatory have been based on 2,476 observations of P and 722 observations of PKP. Of these observations 18.3 per cent have been inconsistent with the published solutions, but a small number of stations have contributed a high percentage of these inconsistencies. Applying a criterion of rejection to the data reduces the percentage of inconsistencies to 14 per cent. Considering that most stations have tried to co�ate as fully as possible in the programme and have reported observations even when the arrivals were recorded only as weakly emergent phases, this percentage seems satisfactorily small. Because the circles represent the boundaries between zones of compression and zones of dilatation, it might be expected that a higher percentage of inconsistencies would occur close to the circles. The reverse has been found; the observations close to the circular boundaries are slightly more accurate than those remote from them. The inconsistent observations show no significant variation with epicentral distance except that the percentage of inconsistencies is high at the shorter distances. This is the effect of the crustal layers, and had been anticipated. There have been 282 observations of PP and 135 observations of pP. These observations were examined to determine whether they could be used to determine the value of Poisson's ratio under the continents and under the oceans. It was found that the percentage of inconsistencies was too high to allow a final conclusion. There were 17 observations of PcP. These were examined following a method suggested by B䳨 in an attempt to define the density ratio at the boundary of the core. The attempt was a failure because of the inconsistency of the data. The failure of the reflected phases suggested that the data from them might be random. To test this, 23 new solutions were carried out based only on P and PKP data. When the solutions were complete, observations for the reflected phases were plotted on the diagrams. It was found that for all reflected phases the inconsistencies approached 50 per cent. It is clear that reflected phases, at least when reported by questionnaires, are not sufficiently accurate to be useful in fault-plane studies.

Polypropylene structural foams: Measurements of the core, skin, and overall mechanical properties with evaluation of predictive models

2016 ◽  
Vol 53 (1) ◽  
pp. 25-44 ◽  
Author(s):  
Tarik Sadik ◽  
Caroline Pillon ◽  
Christian Carrot ◽  
José A Reglero Ruiz ◽  
Michel Vincent ◽  
...  
Keyword(s):  
Mechanical Properties ◽  
Poisson’S Ratio ◽  
Flexural Modulus ◽  
Tensile Modulus ◽  
Poisson's Ratio ◽  
Injection Molding Process ◽  
Mixing Rule ◽  
Molding Process ◽  
Plane Shear ◽  
The Core

Relationships for the prediction of various linear mechanical properties of polymeric sandwich foams obtained in injection processes were studied in comparison with shear, tensile, and flexural tests. The samples were obtained by a core-back foam injection molding process that enables one to obtain sandwich materials with dense skins and a foamed core as revealed by the morphological analysis. Tensile, shear, and flexural moduli were investigated for the skin, the core, and the overall foamed structure. In addition, the Poisson’s ratio of the skin was also determined. The core properties were specifically analyzed by machining the samples and removing the skins. Tensile and shear properties of the core can be well described by the Moore equation. The tensile modulus can be calculated by a linear mixing rule with the moduli of the skin and of the core in relation to the thickness of the layers. Shear and flexural moduli are described by a linear mixing rule on the rigidity in agreement with the mechanics of beams. Tensile modulus, out-of-plane shear modulus, and flexural modulus can finally be predicted by the knowledge of only very few data, namely the tensile modulus and Poisson’s ratio of the matrix, the void fraction, and thickness of the core. The equations were proved to be physically meaningful and consistent with each other.

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.

scholarly journals Oligomodal metamaterials with multifunctional mechanics

2021 ◽  
Vol 118 (21) ◽  
pp. e2018610118
Author(s):  
Aleksi Bossart ◽  
David M. J. Dykstra ◽  
Jop van der Laan ◽  
Corentin Coulais
Keyword(s):  
Poisson’S Ratio ◽  
Shape Change ◽  
Density Ratio ◽  
Deformation Mode ◽  
System Size ◽  
Combinatorial Design ◽  
Poisson's Ratio ◽  
Zero Energy ◽  
Wide Range ◽  
Deformation Modes

Mechanical metamaterials are artificial composites that exhibit a wide range of advanced functionalities such as negative Poisson’s ratio, shape shifting, topological protection, multistability, extreme strength-to-density ratio, and enhanced energy dissipation. In particular, flexible metamaterials often harness zero-energy deformation modes. To date, such flexible metamaterials have a single property, for example, a single shape change, or are pluripotent, that is, they can have many different responses, but typically require complex actuation protocols. Here, we introduce a class of oligomodal metamaterials that encode a few distinct properties that can be selectively controlled under uniaxial compression. To demonstrate this concept, we introduce a combinatorial design space containing various families of metamaterials. These families include monomodal (i.e., with a single zero-energy deformation mode); oligomodal (i.e., with a constant number of zero-energy deformation modes); and plurimodal (i.e., with many zero-energy deformation modes), whose number increases with system size. We then confirm the multifunctional nature of oligomodal metamaterials using both boundary textures and viscoelasticity. In particular, we realize a metamaterial that has a negative (positive) Poisson’s ratio for low (high) compression rate over a finite range of strains. The ability of our oligomodal metamaterials to host multiple mechanical responses within a single structure paves the way toward multifunctional materials and devices.

scholarly journals Fish Cells, a new zero Poisson’s ratio metamaterial—part II: Elastic properties

2020 ◽  
Vol 31 (19) ◽  
pp. 2196-2210
Author(s):  
Mohammad Naghavi Zadeh ◽  
Iman Dayyani ◽  
Mehdi Yasaee
Keyword(s):  
Finite Element ◽  
Shear Modulus ◽  
Elastic Properties ◽  
Transverse Shear ◽  
Poisson’S Ratio ◽  
Shear Loading ◽  
Poisson's Ratio ◽  
Element Analysis ◽  
Plane Shear ◽  
Fish Cells

Fish Cells as a new metamaterial with zero Poisson’s ratio in two planar directions is introduced with application in morphing aircraft skin. In order to tailor the design of this metamaterial for arbitrary loadings, equivalent elastic properties of the Fish Cells metamaterial are derived and analyzed using analytical and numerical methods. The admissible range of geometric parameters is presented and variation of elastic properties with parameters is studied. The effective elastic modulus of the metamaterial is derived analytically and verified with finite element models. The in-plane and transverse shear modulus of the metamaterial are evaluated using finite element analysis where accurate periodic boundary conditions for in-plane shear loading are investigated. The lower and upper bounds of the transverse shear modulus are derived based on strain and complementary energy relations which are verified with finite element results. As zero Poisson’s ratio behavior of the Fish Cells topology is proved, derivative geometries from this topology with zero Poisson’s ratio behavior are also presented.

Dispersive characteristics of the first three Rayleigh modes for a single surface layer

1966 ◽  
Vol 56 (1) ◽  
pp. 43-67 ◽  
Author(s):  
Harold M. Mooney ◽  
Bruce A. Bolt
Keyword(s):  
Surface Layer ◽  
Half Space ◽  
Poisson’S Ratio ◽  
Velocity Ratio ◽  
Surface Displacement ◽  
Shear Velocity ◽  
Poisson's Ratio ◽  
Wave Number ◽  
Model Parameters ◽  
Higher Modes

abstract The dispersive characteristics of a single elastic layer overlying an elastic half-space are examined in detail for the fundamental and the first and second higher modes of Rayleigh waves. Phase velocity, group velocity, and the ratio of horizontal to vertical surface displacement are computed as functions of dimensionless quantities proportional to period and wave number. The significant range for the independent variable, B1T/H, proves to be largely independent of the parameters of the structure. The range is 1 to 20 for the fundamental, 0.3 to cutoff for the first higher mode, and 0.2 to cutoff for the second higher mode. The most important parameter of the structure for Rayleigh wave dispersion is the shear velocity ratio. Variations in the Poisson's ratio in the surface layer and the density contrast may produce substantial effects. Poisson's ratio in the half-space is of least significance. The dependence on model parameters of the long-period cutoff for the higher modes is determined. Specific results are given for the following geophysical examples: continental crust, continental ice cap, sedimentary basin, alluvial overburden, and laboratory seismic models.

The Model for Calculating Elastic Modulus and Poisson's Ratio of Coal Body

2013 ◽  
Vol 6 (1) ◽  
pp. 36-43 ◽  
Author(s):  
Ai Chi ◽  
Li Yuwei
Keyword(s):  
Elastic Modulus ◽  
Poisson’S Ratio ◽  
Fractured Rock ◽  
Rock Block ◽  
Poisson's Ratio ◽  
Linear Elastic ◽  
Study Results ◽  
The Face ◽  
Block Face ◽  
Coal Rock

Coal body is a type of fractured rock mass in which lots of cleat fractures developed. Its mechanical properties vary with the parametric variation of coal rock block, face cleat and butt cleat. Based on the linear elastic theory and displacement equivalent principle and simplifying the face cleat and butt cleat as multi-bank penetrating and intermittent cracks, the model was established to calculate the elastic modulus and Poisson's ratio of coal body combined with cleat. By analyzing the model, it also obtained the influence of the parameter variation of coal rock block, face cleat and butt cleat on the elastic modulus and Poisson's ratio of the coal body. Study results showed that the connectivity rate of butt cleat and the distance between face cleats had a weak influence on elastic modulus of coal body. When the inclination of face cleat was 90°, the elastic modulus of coal body reached the maximal value and it equaled to the elastic modulus of coal rock block. When the inclination of face cleat was 0°, the elastic modulus of coal body was exclusively dependent on the elastic modulus of coal rock block, the normal stiffness of face cleat and the distance between them. When the distance between butt cleats or the connectivity rate of butt cleat was fixed, the Poisson's ratio of the coal body initially increased and then decreased with increasing of the face cleat inclination.

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