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.

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.

Propagation of a Shock Wave Front Through a Lens-Shaped Elastic Body

1974 ◽  
Vol 41 (3) ◽  
pp. 691-696 ◽  
Author(s):  
T. C. T. Ting ◽  
G. Herrmann
Keyword(s):  
Wave Front ◽  
Elastic Body ◽  
Cross Section ◽  
Pressure Pulse ◽  
Time History ◽  
P Wave ◽  
Back Surface ◽  
Ray Theory ◽  
S Wave ◽  
Discontinuous Pressure

Ray theory is used to solve the problem of a plane pressure pulse with a discontinuous pressure front striking an elastic body whose cross section has the shape of a lens. Both plane-strain and axisymmetric motions are considered. The front and back surfaces of the lens are assumed to be circular. The velocity and acceleration at the P-wave front and the discontinuity in acceleration at the S-wave front are obtained explicitly for points along the axis of the lens and at the center of the back surface where reflections occur. The purpose of this study is to assess the effect of the curvatures of the lens on the velocity-time history at the center of the back surface of the lens which can be measured experimentally. Comparison with a laboratory test shows excellent agreement between analytical and experimental results.

Propagation of a Shock Wave Front Across a Curved Fluid-Solid Interface

1976 ◽  
Vol 43 (4) ◽  
pp. 589-593 ◽  
Author(s):  
B. E. Bennett ◽  
G. Herrmann
Keyword(s):  
Shock Wave ◽  
Cross Section ◽  
Pressure Pulse ◽  
Center Line ◽  
Ray Theory ◽  
Reflection And Transmission ◽  
Solid Interface ◽  
Circular Arcs ◽  
Acoustic Fluid ◽  
Special Case

Geometric optics, or the ray theory, is used to investigate the effect of pulse reflection and transmission at a curved fluid-solid interface. In particular, the problem of a plane pressure pulse, supported by an acoustic fluid, impinging on a plane symmetrical elastic body whose cross section is delineated by circular arcs is considered. The response of the solid is determined along its center line to reflection at the back interface with another fluid. Consideration of the special case in which the fluid densities are zero indicates that special care must be exercised in dealing with the in vacuo problem, and particularly in specifying the boundary conditions in that instance.

Extension of forward modeling phase-screen code in isotropic and anisotropic media up to critical angle

Geophysics ◽  
2007 ◽  
Vol 72 (5) ◽  
pp. SM107-SM114 ◽  
Author(s):  
James C. White ◽  
Richard W. Hobbs
Keyword(s):  
Critical Angle ◽  
Model Space ◽  
Anisotropic Media ◽  
Forward Modeling ◽  
Phase Screen ◽  
Computationally Efficient ◽  
Reflection And Transmission ◽  
Transmission Coefficients ◽  
Phase Corrections ◽  
Converted Phases

The computationally efficient phase-screen forward modeling technique is extended to allow investigation of nonnormal raypaths. The code is developed to accommodate all diffracted and converted phases up to critical angle, building on a geometric construction method. The new approach relies upon prescanning the model space to assess the complexity of each screen. The propagating wavefields are then divided as a function of horizontal wavenumber, and each subset is transformed to the spatial domain separately, carrying with it angular information. This allows both locally accurate 3D phase corrections and Zoeppritz reflection and transmission coefficients to be applied. The phase-screen code is further developed to handle simple anisotropic media. During phase-screen modeling, propagation is undertaken in the wavenumber domain where exact expressions for anisotropic phase velocities are available. Traveltimes and amplitude effects from a range of anisotropic shales are computed and compared with previous published results.

Reflection and Transmission Coefficients of Plane Waves in Magnetoelectroelastic Layered Structures

2008 ◽  
Vol 130 (3) ◽  
Author(s):  
J. Y. Chen ◽  
H. L. Chen ◽  
E. Pan
Keyword(s):  
Piezoelectric Materials ◽  
Plane Waves ◽  
Layered Structures ◽  
Organic Glass ◽  
Reflection And Transmission Coefficients ◽  
Material Structure ◽  
Layered System ◽  
Reflection And Transmission ◽  
Transmission Coefficients ◽  
Novel Material

Reflection and transmission coefficients of plane waves with oblique incidence to a multilayered system of piezomagnetic and/or piezoelectric materials are investigated in this paper. The general Christoffel equation is derived from the coupled constitutive and balance equations, which is further employed to solve the elastic displacements and electric and magnetic potentials. Based on these solutions, the reflection and transmission coefficients in the corresponding layered structures are subsequently obtained by virtue of the propagator matrix method. Two layered examples are selected to verify and illustrate our solutions. One is the purely elastic layered system composed of aluminum and organic glass materials. The other layered system is composed of the novel magnetoelectroelastic material and the organic glass. Numerical results are presented to demonstrate the variation of the reflection and transmission coefficients with different incident angles, frequencies, and boundary conditions, which could be useful to nondestructive evaluation of this novel material structure based on wave propagations.

scholarly journals Propagation Characteristics of Oblique Incident Terahertz Wave in Nonuniform Dusty Plasma

2016 ◽  
Vol 2016 ◽  
pp. 1-6 ◽  
Author(s):  
Yunhua Cao ◽  
Haiying Li ◽  
Zhe Wang ◽  
Zhensen Wu
Keyword(s):  
Dusty Plasma ◽  
Terahertz Wave ◽  
Dust Particles ◽  
Number Density ◽  
Propagation Characteristics ◽  
Absorption Coefficients ◽  
Reflection And Transmission ◽  
Transmission Coefficients ◽  
Propagation Matrix ◽  
Transmission And Absorption

Propagation characteristics of oblique incident terahertz wave from the nonuniform dusty plasma are studied using the propagation matrix method. Assuming that the electron density distribution of dusty plasma is parabolic model, variations of power reflection, transmission, and absorption coefficients with frequencies of the incident wave are calculated as the wave illuminates the nonuniform dusty plasma from different angles. The effects of incident angles, number density, and radius of the dust particles on propagation characteristics are discussed in detail. Numerical results show that the number density and radius of the dust particles have very little influences on reflection and transmission coefficients and have obvious effects on absorption coefficients. The terahertz wave has good penetrability in dusty plasma.

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