On whether elastic wave surfaces possess cuspidal edges

1957 ◽  
Vol 53 (4) ◽  
pp. 897-906 ◽  
Author(s):  
M. J. P. Musgrave
Keyword(s):  
Elastic Wave ◽  
Elastic Constants ◽  
Reciprocal Relation ◽  
Sufficient Condition ◽  
Hexagonal Symmetry ◽  
Conical Refraction ◽  
Continuous Sheet ◽  
Cusp Points ◽  
Wave Surfaces ◽  
In Virtue Of

ABSTRACTConsideration of the direction of the normal at any point on a continuous sheet of a surface yields a sufficient condition for the existence of parabolic points on that sheet. This condition has been used to derive some simple inequalities between elastic constants, whose fulfilment determines the existence of parabolic points upon the inverse surfaces of media of orthorhombic, tetragonal, cubic or hexagonal symmetry; in virtue of the polar reciprocal relation between inverse and wave surfaces, the existence of cusp points on the latter is thereby simultaneously established. It is also pointed out that conditions for external conical refraction may prevail in hexagonal media.

On the propagation of elastic waves in aeolotropic media II. Media of hexagonal symmetry

1954 ◽  
Vol 226 (1166) ◽  
pp. 356-366 ◽  
Keyword(s):  
Single Crystal ◽  
Elastic Constants ◽  
Elastic Waves ◽  
Plane Waves ◽  
General Analysis ◽  
Elastic Plane ◽  
Hexagonal Symmetry ◽  
Wave Surfaces ◽  
Propagation Of Elastic Waves

The general analysis presented in part I is here adapted to obtain the velocity, inverse and wave surfaces of a medium of hexagonal symmetry. Values derived from the elastic constants of ( a ) zinc and ( b ) beryl are tabulated and graphs of sections of the surfaces have been drawn. The details of the propagation of elastic plane waves in a single crystal of either substance may be obtained from the data presented.

Elastic-wave surfaces in solids

1982 ◽  
Vol 114 (2) ◽  
pp. 475-480 ◽  
Author(s):  
H. M. Ledbetter ◽  
R. D. Kriz
Keyword(s):  
Elastic Wave ◽  
Wave Surfaces

Effect of an elastically restrained boundary on SV-wave radiation patterns

1968 ◽  
Vol 58 (2) ◽  
pp. 497-520
Author(s):  
Y. T. Huang
Keyword(s):  
Boundary Condition ◽  
Wave Propagation ◽  
Free Boundary ◽  
Boundary Conditions ◽  
Elastic Wave ◽  
Solid Earth ◽  
Elastic Constants ◽  
Wave Radiation ◽  
Free Boundary Conditions ◽  
Elastically Restrained

Abstract In the solution of elastic wave propagation equations applied to solid earth, it is customarily assumed that free boundary conditions are satisfied at a surface which is in contact with the atmosphere. Situations which depart from this boundary condition have now been studied for arbitrary combinations of the Lamé elastic constants. The solutions are given for a homogeneous, isotropic half space.

scholarly journals Sound velocities and Debye temperature of BeSe under high pressure up to 50 GPa

2016 ◽  
Vol 5 (1) ◽  
pp. 7
Author(s):  
Salah Daoud
Keyword(s):  
High Pressure ◽  
Elastic Wave ◽  
Mechanical Behavior ◽  
Debye Temperature ◽  
Elastic Constants ◽  
Structural Parameters ◽  
Theoretical Data ◽  
Elastic Wave Velocity ◽  
Brittle Behavior ◽  
Sound Velocities

The mechanical behavior, sound velocities and Debye temperature of beryllium-selenide (BeSe) semiconductor under pressure up to 50 GPa have been estimated using the structural parameters and elastic constants of Fanjie Kong and Gang Jiang (Physica B 404 (2009) 3935-3940). The Pugh ratio, the directional dependence of elastic wave velocity, the longitudinal, transverse and average sound velocities, and the Debye temperature are successfully predicted and analyzed in comparison with the available theoretical data. The analysis of the Pugh ratio indicates that this compound is prone to brittle behavior. Our obtained results of the longitudinal, transverse and average sound velocities at high pressure indicate that these of Kong and Jiang (Physica B 404 (2009) 3935-3940) are not correctly predicted.

scholarly journals GEODYNAMICS

GEODYNAMICS ◽  
2011 ◽  
Vol 2(11)2011 (2(11)) ◽  
pp. 251-253
Author(s):  
H. T. Prodaivoda ◽  
◽  
S. A. Vyzhva ◽  
Yu. A. Onanko ◽  
A. P. Onanko ◽  
...  
Keyword(s):  
Elastic Wave ◽  
Elastic Constants ◽  
Elastic Symmetry ◽  
Wave Velocities ◽  
Anisotropy Parameters ◽  
Non Destructive

The elastic constants are appraised sandstones of Volino – Podolskiy region, which testify that elastic symmetry is orthorhombic. The anisotropy parameters of rock-collectors are explored from the ultrasonic results measurements of elastic wave velocities. The method of measurings of anisotropy parameters of elastic wave velocities is offered for non-destructive control of structure of sandstones.

scholarly journals On three-stage temperature dependence of elastic wave velocities for rocks

2021 ◽  
Vol 18 (3) ◽  
pp. 328-338
Author(s):  
Nianqi Li ◽  
Li-Yun Fu ◽  
Jian Yang ◽  
Tongcheng Han
Keyword(s):  
Elastic Wave ◽  
Temperature Dependence ◽  
Elastic Constants ◽  
Nonlinear Behavior ◽  
P Wave ◽  
Shape Model ◽  
Wave Velocities ◽  
Nonlinear Thermoelasticity ◽  
Velocity Variations ◽  
Shape Curve

Abstract For most rocks, the typical temperature behavior of elastic wave velocities generally features a three-stage nonlinear characteristic that could be expressed by a reverse S-shape curve with two inflexion points. The mechanism regulating the slow-to-fast transition of elastic constants remains elusive. The physics of critical points seems related to the multimineral composition of rocks with differentiated thermodynamic properties. Based on laboratory experiments for several rocks with different levels of heterogeneity in compositions, we conduct theoretical and empirical simulations by nonlinear thermoelasticity methods and a S-shape model, respectively. The classical theory of linear thermoelasticity based on the Taylor expansion of strain energy functions has been widely used for crystals, but suffers from a deficiency in describing thermal-associated velocity variations for rocks as a polycrystal mixture. Current nonlinear thermoelasticity theory describes the third-order temperature dependence of velocity variations by incorporating the fourth-order elastic constants. It improves the description of temperature-induced three-stage velocity variations in rocks, but involves with some divergences around two inflexion points, especially at high temperatures. The S-shape model for empirical simulations demonstrates a more accurate depiction of thermal-associated three-stage variations of P-wave velocities. We investigate the physics of the parameters ${a_1}$ and ${b_1}$ in the S-shape model. These fitting parameters are closely related to thermophysical properties by being proportional to the specific heat and thermal conductivity of rocks. We discuss the mechanism that regulates the slow-to-fast transition in the three-stage nonlinear behavior for various rocks.

Axisymmetric Free Vibrations of a Transversely Isotropic Finite Cylindrical Rod

1988 ◽  
Vol 55 (4) ◽  
pp. 855-862 ◽  
Author(s):  
C. P. Lusher ◽  
W. N. Hardy
Keyword(s):  
Boundary Conditions ◽  
Elastic Constants ◽  
Transversely Isotropic ◽  
Acoustic Vibration ◽  
Elastic Cylinder ◽  
Free Vibrations ◽  
Mode Shapes ◽  
Hexagonal Symmetry ◽  
Hexagonal System ◽  
Better Than

The frequencies of free vibration and mode shapes are calculated for axisymmetric modes of an elastic cylinder of finite length having hexagonal symmetry with the crystallographic c-axis coincident with the axis of the cylinder (a transversely isotropic finite cylindrical rod). A series solution is used which satisfies term-by-term the differential equations of linear elasticity and the boundary conditions on the shear stress; the boundary conditions on the normal stresses are satisfied by using an orthogonalization procedure. As an example, the method is applied to sapphire, with one of the six elastic constants (c14) taken to be zero. The other five elastic constants are those of the hexagonal system. The calculated acoustic vibration frequencies agree to better than 1 percent with measurements made on sapphire at room temperature, for a cylinder of half-height to radius ratio ∼ 1.

Thermoelastic Properties of (Mg,Fe)SiO3 Perovskite

2002 ◽  
Vol 718 ◽  
Author(s):  
Boris Kiefer ◽  
Lars Stixrude
Keyword(s):  
Elastic Wave ◽  
Elastic Properties ◽  
Solid Solutions ◽  
Elastic Constants ◽  
Lower Mantle ◽  
High Pressures ◽  
Thermoelastic Properties ◽  
Wave Velocities ◽  
Lateral Variations ◽  
Iron Bearing

AbstractMagnesium rich (Mg1-x,Fex perovskite is thought to be the most abundant mineral in the earth's lower mantle between 660 km and 2900 km depth. We discuss (mg,Fe) solid solutions and their elastic properties at lower mantle pressures. The diffrences of the elastic constants between the Mg-endmember and the iron bearing perovskite with x=0.25 are used to predict the compositional contribution to lateral variations of elastic wave-velocities at high pressures. These predictions are compared and discussed in the context of seismic observations.

Cuspidal edges for elastic wave surfaces for cubic crystals

Pramana ◽  
1977 ◽  
Vol 8 (4) ◽  
pp. 348-362 ◽  
Author(s):  
Jacob Philip ◽  
K S Viswanathan
Keyword(s):  
Elastic Wave ◽  
Cubic Crystals ◽  
Wave Surfaces
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