REFLECTION AND TRANSMISSION COEFFICIENTS FOR PLANE WAVES IN ELASTIC MEDIA

Geophysics ◽  
1940 ◽  
Vol 5 (2) ◽  
pp. 115-148 ◽  
Author(s):  
M. Muskat ◽  
M. W. Meres
Keyword(s):  
Incident Energy ◽  
Plane Waves ◽  
Total Reflection ◽  
Interfacial Velocity ◽  
Reflection And Transmission ◽  
Transverse Waves ◽  
Longitudinal Waves ◽  
Transmission Coefficients ◽  
Elastic Interfaces ◽  
Density Ratios

The results are given of a systematic series of calculations on the coefficients of reflection and transmission for plane waves incident on elastic interfaces. Tables are given for the amplitudes of the reflected and transmitted longitudinal and transverse waves, for the intensities of these components, and for the fractions of the incident energy carried away by them. For incident longitudinal waves calculations were carried out for angles of incidence between 0 and 30 with 5° intervals. For incident transverse waves polarized in the plane of incidence results are given for four angles of incidence up to approximately 16°. For incident transverse waves polarized normal to the plane of incidence the calculations were carried through for all angles of incidence—in steps of 5°—up to total reflection. All the calculations were carried through for interfacial density ratios of 0.7 to 1.3 in steps of 0.1, and interfacial velocity ratios between 0.5 and 2.0 in steps of 0.25.

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.

THE SEISMIC WAVE ENERGY REFLECTED FROM VARIOUS TYPES OF STRATIFIED HORIZONS

Geophysics ◽  
1940 ◽  
Vol 5 (2) ◽  
pp. 149-155 ◽  
Author(s):  
M. Muskat ◽  
M. W. Meres
Keyword(s):  
Seismic Wave ◽  
Wave Energy ◽  
Incident Energy ◽  
Preceding Paper ◽  
Reflection And Transmission Coefficients ◽  
Angle Of Incidence ◽  
Reflection And Transmission ◽  
Transmission Coefficients

Two applications are made of the reflection and transmission coefficients reported in the preceding paper. These concern the effect of the angle of incidence upon the fraction of incident energy returning to the surface, and the effect of velocity stratification upon the energy return.

scholarly journals Propagation of Plane Waves in a Thermally Conducting Mixture

2011 ◽  
Vol 2011 ◽  
pp. 1-12
Author(s):  
Baljeet Singh
Keyword(s):  
Free Surface ◽  
Longitudinal Wave ◽  
Plane Waves ◽  
Generalized Thermoelasticity ◽  
Elastic Solid ◽  
Reflection Coefficients ◽  
Governing Equations ◽  
Transverse Waves ◽  
Longitudinal Waves ◽  
Thermally Conducting

The governing equations for generalized thermoelasticity of a mixture of an elastic solid and a Newtonian fluid are formulated in the context of Lord-Shulman and Green-Lindsay theories of generalized thermoelasticity. These equations are solved to show the existence of three coupled longitudinal waves and two coupled transverse waves, which are dispersive in nature. Reflection from a thermally insulated stress-free surface is considered for incidence of coupled longitudinal wave. The speeds and reflection coefficients of plane waves are computed numerically for a particular model.

Ray-synthetic seismograms for SH waves in anelastic media

1980 ◽  
Vol 70 (1) ◽  
pp. 29-46
Author(s):  
E. S. Krebes ◽  
F. Hron
Keyword(s):  
Plane Waves ◽  
Synthetic Seismograms ◽  
Body Waves ◽  
Plane Boundary ◽  
Theory Approach ◽  
Reflection And Transmission ◽  
Sh Waves ◽  
Transmission Coefficients ◽  
Mathematical Properties ◽  
Crustal Model

abstract The linear theory of viscoelasticity is used to study the effects of anelasticity on SH body waves propagating through a layered medium. The mathematical properties of SH waves in a viscoelastic medium are outlined. Reflection and transmission coefficients for SH plane waves impinging upon a plane boundary separating two anelastic media are calculated and compared with the coefficients for the perfectly elastic case. Synthetic seismograms for teleseismic SH body waves are computed for a plane-layered crustal model in both the elastic and anelastic cases, using a ray theory approach.

Wave Propagation Analysis of an Axially Strained, Rotating Timoshenko Shaft: Part I

1997 ◽  
Author(s):  
Bongsu Kang ◽  
Chin An Tan
Keyword(s):  
Wave Reflection ◽  
Rotation Speed ◽  
Arbitrary Point ◽  
Axial Deformation ◽  
Rotating Shaft ◽  
Frequency Spectra ◽  
Reflection And Transmission ◽  
Transverse Waves ◽  
Transmission Coefficients ◽  
Axial Forces

Abstract In this paper, transverse waves propagating in an infinitely long, rotating Timoshenko shaft subjected to axial forces are studied. The model includes the contributions of axial deformation to the transverse vibration of the rotating shaft. Four different types of wave motions, two cutoff frequencies and frequency spectra are defined and discussed. The wave reflection and transmission characteristics of the shaft at arbitrary point supports are also examined by deriving the reflection and transmission matrices for an incident waves upon a general intermediate support. Numerical results showing the effects of axial force, shaft rotation speed, shear deformation, and rotary inertia on the wave reflection and transmission coefficients for classical supports are presented for both the Timoshenko and Euler-Bernoulli beams. It is found that the wave motions are generally independent of the rotation speed and the axial load affects significantly the wave motions at small real wavenumbers.

scholarly journals A trace formula for schrödinger operators with step potentials

1982 ◽  
Vol 24 (2) ◽  
pp. 138-159 ◽  
Author(s):  
D. M. O'Brien
Keyword(s):  
Compact Support ◽  
Plane Waves ◽  
Schrödinger Operators ◽  
Schrodinger Operators ◽  
Step Potential ◽  
Reflection And Transmission ◽  
One Dimensional ◽  
Transmission Coefficients ◽  
Simple Step ◽  
Infinitely Differentiable Function

AbstractThis paper shows how to compute the trace of G(T) – G(T0), where G is an infinitely differentiable function with compact support, and where T and T0 are one-dimensional Schrödinger operators on (−∞, ∞) with potentials q and q0. It is assumed that q0 is a simple step potential and that q decays exponentially to q0. The trace is expressed in terms of the reflection and transmission coefficients for the scattering of plane waves by the potential q.

scholarly journals Reection and refraction of plane waves at the interface between magnetoelectroelastic and liquid media

2013 ◽  
Vol 40 (3) ◽  
pp. 427-439 ◽  
Author(s):  
Rong Zhang
Keyword(s):  
Liquid Medium ◽  
Incident Angle ◽  
Plane Waves ◽  
Transversely Isotropic ◽  
Liquid Media ◽  
Reflection And Transmission ◽  
Transmission Coefficients ◽  
Reflection And Refraction ◽  
Acoustic Device ◽  
Wave Incidence

This paper analyzes the reflection and refraction of plane wave incidences at the interface between magnetoelectroelastic (MEE) and liquid media. The MEE medium is assumed to be transversely isotropic and the liquid medium to be nonviscous. Three cases, i.e., the coupled quasipressure wave incidence from the MEE medium, the coupled quasi-shear vertical wave incidence from the MEE medium, and the pressure wave incidence from the liquid medium, are discussed. The expressions of reflection and transmission coefficients varying with the incident angle are obtained. This investigation would be useful to the MEE acoustic device field.

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