Explicit formulas for the reflection and transmission coefficients of one-component waves through a stack of an arbitrary number of layers

Wave Motion ◽  
2015 ◽  
Vol 54 ◽  
pp. 134-144 ◽  
Author(s):  
Pham Chi Vinh ◽  
Tran Thanh Tuan ◽  
Marcos A. Capistran
Keyword(s):  
Arbitrary Number ◽  
Reflection And Transmission Coefficients ◽  
Explicit Formulas ◽  
Reflection And Transmission ◽  
Transmission Coefficients ◽  
Number Of Layers

Body waves in a “real Earth”. Part I

1973 ◽  
Vol 63 (1) ◽  
pp. 145-156 ◽  
Author(s):  
A. Cisternas ◽  
O. Betancourt ◽  
A. Leiva
Keyword(s):  
Exact Solution ◽  
Theoretical Analysis ◽  
Power Series ◽  
Arbitrary Number ◽  
Body Waves ◽  
Reflection And Transmission Coefficients ◽  
Earth Model ◽  
Reflection And Transmission ◽  
Transmission Coefficients ◽  
The Earth

abstract A theoretical analysis of body waves in a “real Earth” is presented. The earth model consists of an arbitrary number of spherical liquid and solid layers. The algebraic part of the analysis deals with the way to obtain generalized rays out of the exact solution. It is shown that the Rayleigh matrix, and not the Rayleigh determinant, should be used to expand the solution into a power series of modified reflection and transmission coefficients in order to obtain rays.

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 Estimation of S-parameters and dielectric permittivity of quartz ceramics samples in millimeter waveband

Doklady BGUIR ◽  
2021 ◽  
Vol 19 (7) ◽  
pp. 65-71
Author(s):  
N. A. Pevneva ◽  
D. A. Kondrashov ◽  
A. L. Gurskii ◽  
A. V. Gusinsky
Keyword(s):  
Dielectric Constant ◽  
Dielectric Permittivity ◽  
Ceramic Materials ◽  
Reflection And Transmission Coefficients ◽  
Frequency Range ◽  
Reflection And Transmission ◽  
Transmission Coefficients ◽  
Higher Order Modes ◽  
S Parameters ◽  
The Fourier Transform

A modified Nicholson – Ross – Weir method was used to determine complex parameters and dielectric permittivity of ceramic materials in the range 78.33–118.1 GHz. The measuring equipment is a meter of complex reflection and transmission coefficients, a waveguide measuring canal with a special measuring cell, consisting of two irregular waveguides and a waveguide chamber between them, which provides insignificant influence of higher-order modes. The dependences of the amplitude and phase of the reflection and transmission coefficients on frequency were obtained experimentally for fluoroplastic and three ceramic samples in the frequency range 78.33–118.1 GHz. The obtained S-parameters are processed according to an algorithm that includes their averaging based on the Fourier transform in order to obtain the values of the dielectric permittivity. Fluoroplastic was used as a reference material with a known dielectric constant. The dielectric constant of fluoroplastic has a stable value of 2.1 in the above mentioned frequency range. The dielectric constant of sample No. 1 varies from 3.6 to 2.5 at the boundaries of the range, sample No. 2 – from 3.7 to 2.1, sample No. 3 – from 2.9 to 1.5. The experimental data are in satisfactory agreement with the literature data for other frequencies taking into account the limits set by the measurement uncertainty.

scholarly journals Homogenization of very rough three-dimensional interfaces for the poroelasticity theory with Biot's model

2019 ◽  
Author(s):  
Nguyen Thi Kieu ◽  
Pham Chi Vinh ◽  
Do Xuan Tung
Keyword(s):  
Incident Angle ◽  
Three Dimensional ◽  
Homogenization Method ◽  
Reflection And Transmission Coefficients ◽  
Biot Theory ◽  
Rough Interface ◽  
Matrix Formulation ◽  
Reflection And Transmission ◽  
Transmission Coefficients ◽  
The Matrix

In this paper, we carry out the homogenization of a very rough three-dimensional interface separating  two dissimilar generally anisotropic poroelastic solids modeled by the Biot theory. The very rough interface is assumed to be a cylindrical surface that rapidly oscillates between two parallel planes, and the motion is time-harmonic. Using the homogenization method with the matrix formulation of the poroelasicity theory, the explicit  homogenized equations have been derived. Since the obtained  homogenized equations are totally explicit, they are very convenient for solving various practical problems. As an example proving this, the reflection and transmission of SH waves at a very rough interface of tooth-comb type is considered. The closed-form analytical expressions of the reflection and transmission coefficients have been  derived. Based on them, the effect of the incident angle and some material parameters  on the reflection and transmission coefficients are examined numerically.

Sign in / Sign up

Export Citation Format

Share Document