Propagation of Stress Gradient Through an Inclusion—Part 1

1973 ◽  
Vol 40 (3) ◽  
pp. 711-717 ◽  
Author(s):  
T. C. T. Ting ◽  
Shun-Chin Chou
Keyword(s):  
Composite Materials ◽  
Wave Front ◽  
Incident Wave ◽  
Stress Gradient ◽  
Higher Order ◽  
Elastic Media ◽  
Interface Boundary ◽  
Reflection And Transmission ◽  
Transmission Coefficients ◽  
Derivatives Of

This is the first of a two-part study on the propagation of stress gradient in composite materials. Both the plane-strain and axisymmetric motions are considered. In this paper, the reflection and transmission coefficients are derived for the stress, the stress gradient, and the higher-order derivatives of stress at an interface between two elastic media. It is shown that while the reflection and transmission of the stress do not depend on the geometries of the incident wave front and the interface boundary, the reflection and transmission of the stress gradient, and the higher-order derivatives of stress do depend on these geometries. Explicit expressions are derived for the reflection and transmission of the stress gradient in terms of the radii of curvatures of the incident wave front and the interface boundary.

Wave-Front Analysis in Composite Materials

1969 ◽  
Vol 36 (3) ◽  
pp. 497-504 ◽  
Author(s):  
T. C. T. Ting ◽  
E. H. Lee
Keyword(s):  
Wave Front ◽  
Pressure Pulse ◽  
Spherical Inclusion ◽  
Stress Gradient ◽  
Back Surface ◽  
Ray Theory ◽  
Reflection And Transmission ◽  
Transmission Coefficients ◽  
Linear Elastic ◽  
Elastic Composite

The propagation of an initially sharp plane pressure pulse through a linear elastic composite medium is analyzed. Wave front and ray theory analogous to geometrical optics is shown to determine the change in shape of the leading wave front and also the stresses immediately behind it. For certain circumstances the stress amplitudes on this front, or the corresponding tensile stresses on its reflection at the free back surface of a slab, may be critical in design. Examples are presented of an initially sharp plane pressure pulse transmitted through an elastic circular cylinder and an elastic spherical inclusion. The method can be applied to more general composite configurations, and can be extended to determine the stress gradient behind the front. For the latter, general formulas are derived by which the reflection and transmission coefficients can be determined for the stress gradient and the higher-order derivatives at an arbitrary interface.

SS-traveltime parameters from PP and PS reflections

Geophysics ◽  
2009 ◽  
Vol 74 (4) ◽  
pp. R35-R47 ◽  
Author(s):  
Bjørn Ursin ◽  
Martin Tygel ◽  
Einar Iversen
Keyword(s):  
Velocity Model ◽  
Ocean Bottom ◽  
Reflection And Transmission ◽  
Transmission Coefficients ◽  
Partial Reconstruction ◽  
Propagator Matrix ◽  
Geometric Spreading ◽  
Derivatives Of ◽  
Full Simulation ◽  
Original Formula

The SS-wave traveltimes can be derived from PP- and PS-wave data with the previously derived [Formula: see text] method. We have extended this method as follows. (1) The previous requirement that sources and receivers be located on a common acquisition surface is removed, which makes the method directly applicable to PS-waves recorded on the ocean bottom and PP-waves recorded at the ocean surface. (2) By using the concept and properties of surface-to-surface propagator matrices, the second-order traveltime derivatives of the SS-waves are obtained. In the same way as for the original [Formula: see text] method, the proposed extension is valid for arbitrary anisotropic media. The propagator matrix and geometric spreading of an SS-wave reflected at a given point on a target reflector are obtained explicitly from the propagators of the PP- and PS-waves reflected at the same point. These additional parameters provided by the extended [Formula: see text] method can be used for a partial reconstruction of the SS-wave amplitude as well as for tomographic estimation of the elastic velocity model. A full simulation of the SS-wave, which includes reflection and transmission coefficients, cannot be obtained directly from recorded PP- and PS-wave amplitudes.

scholarly journals Reflection and transmission of P-waves at a very rough interface between two isotropic elastic solids

2021 ◽  
Author(s):  
Pham Chi Vinh ◽  
Do Xuan Tung ◽  
Nguyen Thi Kieu
Keyword(s):  
Incident Wave ◽  
Elastic Layer ◽  
Incident Angle ◽  
P Wave ◽  
Rough Interface ◽  
Elastic Solids ◽  
P Waves ◽  
Reflection And Transmission ◽  
Reflected Waves ◽  
Transmission Coefficients

This paper deals with the reflection and transmission of P-waves at a very rough interface between two isotropic elastic solids. The interface is assumed to oscillate between two straight lines. By mean of homogenization, this problem is reduced to the reflection and transmission of P-waves through an inhomogeneous orthotropic elastic layer. It is shown that a P incident wave always creates two reflected waves (one P wave and one SV wave), however, there may exist two, one or no transmitted waves. Expressions in closed-form of the reflection and transmission coefficient have been derived using the transfer matrix of an orthotropic elastic layer. Some numerical examples are carried out to examine the reflection and transmission of P-waves at a very rough interface of tooth-comb type, tooth-saw type and sin type. It is found numerically that the reflection and transmission coefficients depend strongly on the incident angle, the incident wave frequency, the roughness and the type of interfaces.

Reflection and transmission of surface waves at a vertical interface in anisotropic elastic media

1993 ◽  
Vol 83 (5) ◽  
pp. 1355-1372
Author(s):  
E. N. Its ◽  
J. S. Lee
Keyword(s):  
Surface Waves ◽  
Wave Reflection ◽  
Analytical Procedure ◽  
Far Field ◽  
Elastic Media ◽  
Reflection And Transmission ◽  
Trade Off ◽  
Transmission Coefficients ◽  
Dyadic Representation ◽  
Anisotropic Elastic

Abstract Propagation of surface waves across a vertical interface between anisotropic blocks is considered in this paper. Dyadic representation of a far field Green's function for an anisotropic half-space is constructed first. An analytical procedure is then developed to determine the reflection and transmission coefficients of surface waves at the vertical interface between two laterally homogeneous anisotropic quarter-spaces. Numerical results of Rayleigh wave reflection at vertical interfaces between dissimilar blocks are presented and the trade-off between anisotropy and inhomogeneity is discussed.

The viscoelastic reflection/transmission problem: Two special cases

1983 ◽  
Vol 73 (6A) ◽  
pp. 1673-1683
Author(s):  
E. S. Krebes
Keyword(s):  
Incident Wave ◽  
Incidence Angle ◽  
Reflection And Transmission Coefficients ◽  
Reflection And Transmission ◽  
Transmission Coefficients ◽  
First Case ◽  
Special Cases ◽  
Mathematical Formulas ◽  
Linear Viscoelastic ◽  
Ray Bending

Abstract In the general problem of plane wave reflection and transmission at a boundary separating two linear viscoelastic media, the mathematical formulas for the reflection and transmission coefficients, the transmission angle, the attenuation vector, etc., are not easily interpretable because they cannot easily be expressed in terms of the basic input parameters (Q, incidence angle, etc.). To gain further insight, we study two special cases in which mathematical simplifications occur. No low-loss approximations are involved. In the first case, the incident wave is homogeneous, and the Q values of the two layers are equal, and we find, among other things, that the reflection and transmission coefficients are the same as the ones for perfect elasticity (they do not involve complex velocities, etc., and are independent of Q). In the second special case, the degree of inhomogeneity of the incident wave approaches its upper limit, and we find that the reflection and transmission coefficients approach constant (complex) values independent of the incidence angle, and that there is almost no ray-bending (refraction) upon transmission of the incident wave through the boundary.

Tunable and Self-Sensing Microwave Composite Materials Incorporating Ferromagnetic Microwires

2008 ◽  
Vol 54 ◽  
pp. 201-210 ◽  
Author(s):  
Dmitriy Makhnovskiy ◽  
Arkadi Zhukov ◽  
V. Zhukova ◽  
J. Gonzalez
Keyword(s):  
Magnetic Field ◽  
Composite Materials ◽  
External Magnetic Field ◽  
Resonance Frequency ◽  
Free Space ◽  
Effective Permittivity ◽  
Stress Sensitivity ◽  
Reflection And Transmission Coefficients ◽  
Reflection And Transmission ◽  
Transmission Coefficients

New types of stress sensitive and magnetic field tunable microwave composite materials are discussed where embedded short ferromagnetic microwire inclusions are used as controllable radiative elements. The dc external magnetic field is applied to the whole composite structure. And, the local stress is transferred to the individual microwires through the accommodating composite matrix. The spatial and angular distributions of microwires can be random, partly ordered, or completely ordered. For a wide frequency range, the free-space microwave response of a wire-filled composite can be characterized by a complex effective permittivity with resonance frequency dispersion. The latter depends on the conductive and magnetic properties of the microwire inclusions that contribute to the ac microwire magnetoimpedance (MI). In the vicinity of the so-called antenna resonance frequency, which is defined by the length of microwires and matrix dielectric constant, any variations in the MI of the microwires will result in large changes of the effective permittivity, and hence the reflection and transmission coefficients for an incident microwave. The field or stress dependence of the effective permittivity arises from the corresponding field or stress sensitivity of the MI in the ferromagnetic microwires with induced circumferential or helical magnetic anisotropy, respectively. The strong field tunable effect in the proposed composite materials can be utilized to introduce reconfigurable microwave properties in coatings, absorbers, and randomizers, and also in new media such as microwave metamaterials and bandgap wire structures. A maximum field tunability of 30 dB was achieved for free-space transmission measurements when the external magnetic field changed from zero to ~40 Oe. The stress sensitivity of reflection and transmission coefficients opens up new possibilities for the distant non-destructive testing and evaluation of composite materials both in the laboratory environment and large scale applications. The stress tunability of transmission coefficient may reach up to 5-8 dB within the elastic limit. The reflection coefficient usually demonstrates less tunability in both cases (field and stress dependent) and may require a multilayer structure to achieve better results, but it is always strong enough for the stress sensing applications.

The scattering by a dielectric spheroid of an electromagnetic surface wave travelling along a duct

1984 ◽  
Vol 391 (1800) ◽  
pp. 181-199 ◽  
Keyword(s):  
Surface Wave ◽  
Incident Wave ◽  
Wave Mode ◽  
Reflection And Transmission Coefficients ◽  
Leading Order ◽  
Reflection And Transmission ◽  
Transmission Coefficients ◽  
Electromagnetic Surface Wave

An electromagnetic surface wave travelling between conducting walls is incident on a small dielectric axisymmetric spheroid. Reflection and transmission coefficients are found, to leading order, by a considerable generalization of the method used in an earlier paper. The possibility of zero reflection of the incident wave mode is investigated.

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