Boundary conditions for a fluid‐saturated porous solid

Geophysics ◽  
1987 ◽  
Vol 52 (2) ◽  
pp. 174-178 ◽  
Author(s):  
Oscar M. Lovera
Keyword(s):  
Boundary Conditions ◽  
Total Energy ◽  
Elastic Medium ◽  
Contact Surface ◽  
Normal Component ◽  
Porous Solid ◽  
Reflection And Transmission ◽  
Transmission Coefficients ◽  
Contact Surfaces ◽  
Transmission And Reflection

Using Biot’s theory, a set of boundary conditions is presented for wave transmission and reflection at the contact surface between an elastic medium (fluid or solid) and a fluid‐saturated porous solid (Biot medium). The analysis shows the continuity of the normal component of the density energy flux vectors across the contact surfaces, so that total energy is preserved. Energy reflection and transmission coefficients are computed for each kind of Biot wave.

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

1997 ◽  
Author(s):  
Bongsu Kang ◽  
Chin An Tan
Keyword(s):  
Boundary Conditions ◽  
Wave Reflection ◽  
Axial Strain ◽  
Free Vibration Analysis ◽  
Reflection And Transmission ◽  
Transmission Coefficients ◽  
Propagation Analysis ◽  
Geometric Discontinuities ◽  
Bernoulli Models ◽  
Incident Waves

Abstract In this paper, the wave reflection and transmission characteristics of an axially strained, rotating Timoshenko shaft under general support and boundary conditions, and with geometric discontinuities are examined. As a continuation to Part I of this paper (Kang and Tan, 1997), the wave reflection and transmission at point supports with finite translational and rotational constraints are further discussed. The reflection and transmission matrices for incident waves upon general supports and geometric discontinuities are derived. These matrices are combined, with the aid of the transfer matrix method, to provide a concise and systematic approach for the free vibration analysis of multi-span rotating shafts with general boundary conditions. Results on the wave reflection and transmission coefficients are presented for both the Timoshenko and the Euler-Bernoulli models to investigate the effects of the axial strain, shaft rotation speed, shear and rotary inertia.

scholarly journals The Scattering and Bound States of the Schrödinger Particle in Generalized Asymmetric Manning-Rosen Type Potential

2014 ◽  
Vol 2014 ◽  
pp. 1-10 ◽  
Author(s):  
Ahmet Taş ◽  
Soner Alpdoğan ◽  
Ali Havare
Keyword(s):  
Bound States ◽  
Reflection And Transmission ◽  
Transmission Coefficients ◽  
Transmission And Reflection Coefficients ◽  
Scattering States ◽  
Different Types ◽  
Nonrelativistic Quantum Mechanics ◽  
Application Fields ◽  
Type Potential ◽  
Transmission And Reflection

We solve exactly one-dimensional Schrödinger equation for the generalized asymmetric Manning-Rosen (GAMAR) type potential containing the different types of physical potential that have many application fields in the nonrelativistic quantum mechanics and obtain the solutions in terms of the Gauss hypergeometric functions. Then we determine the solutions for scattering and bound states. By using these states we calculate the reflection and transmission coefficients for scattering states and achieve a correlation that gives the energy eigenvalues for the bound states. In addition to these, we show how the transmission and reflection coefficients depend on the parameters which describe shape of the GAMAR type potential and compare our results with the results obtained in earlier studies.

scholarly journals Interaction acoustic waves with a layered structure containing layer of bubbly liquid

2018 ◽  
Vol 148 ◽  
pp. 15006
Author(s):  
Damir Gubaidullin ◽  
Anatolii Nikiforov
Keyword(s):  
Acoustic Waves ◽  
Theoretical Study ◽  
Bubbly Liquid ◽  
Air Bubbles ◽  
Angle Of Incidence ◽  
Natural Oscillations ◽  
Reflection And Transmission ◽  
Transmission Coefficients ◽  
Gel Layer ◽  
Transmission And Reflection

The results of a theoretical study of the effect of a bubble layer on the propagation of acoustic waves through a thin three-layered barrier at various angles of incidence are presented. The barrier consists of a layer of gel with polydisperse air bubbles bounded by layers of polycarbonate. It is shown that the presence of polydisperse air bubbles in the gel layer significantly changes the transmission and reflection of the acoustic signal when it interacts with such an obstacle for frequencies close to the resonant frequency of natural oscillations of the bubbles. The frequency range is identified where the angle of incidence has little effect on the reflection and transmission coefficients of acoustic waves.

scholarly journals FAST SOLITONS ON STAR GRAPHS

2011 ◽  
Vol 23 (04) ◽  
pp. 409-451 ◽  
Author(s):  
RICCARDO ADAMI ◽  
CLAUDIO CACCIAPUOTI ◽  
DOMENICO FINCO ◽  
DIEGO NOJA
Keyword(s):  
Solitary Wave ◽  
Boundary Conditions ◽  
Linear Problem ◽  
Cubic Nonlinearity ◽  
Point Interactions ◽  
Reflection And Transmission ◽  
Seminal Paper ◽  
Star Graphs ◽  
Transmission Coefficients ◽  
Energy Domain

We define the Schrödinger equation with focusing, cubic nonlinearity on one-vertex graphs. We prove global well-posedness in the energy domain and conservation laws for some self-adjoint boundary conditions at the vertex, i.e. Kirchhoff boundary condition and the so-called δ and δ′ boundary conditions. Moreover, in the same setting, we study the collision of a fast solitary wave with the vertex and we show that it splits in reflected and transmitted components. The outgoing waves preserve a soliton character over a time which depends on the logarithm of the velocity of the ingoing solitary wave. Over the same timescale, the reflection and transmission coefficients of the outgoing waves coincide with the corresponding coefficients of the linear problem. In the analysis of the problem, we follow ideas borrowed from the seminal paper [17] about scattering of fast solitons by a delta interaction on the line, by Holmer, Marzuola and Zworski. The present paper represents an extension of their work to the case of graphs and, as a byproduct, it shows how to extend the analysis of soliton scattering by other point interactions on the line, interpreted as a degenerate graph.

Transmission and Reflection Coefficients for Damage Identification in 1D Elements

2009 ◽  
Vol 413-414 ◽  
pp. 95-100 ◽  
Author(s):  
Marek Krawczuk ◽  
Magdalena Palacz ◽  
Arkadiusz Zak ◽  
Wiesław M. Ostachowicz
Keyword(s):  
Damage Identification ◽  
Reflection And Transmission Coefficients ◽  
Reflection Coefficients ◽  
Reflection And Transmission ◽  
Transmission Coefficients ◽  
Transmission And Reflection Coefficients ◽  
Structural Discontinuity ◽  
Spectral Finite Element ◽  
Processing Techniques ◽  
Transmission And Reflection

According to the latest research results presented in the literature changes in propagating waves are one of the most promising parameters for damage identification algorithms. Numerous publications describe methods of damage identification based on the analysis of signals reflected from damage. They also include complicated signal processing techniques. Such methods work well for damage localisation, but it is rather difficult to use them in order to estimate the size of damage. It is natural that propagating wave reflects from any structural discontinuity. The bigger the disturbance the bigger part of a propagating wave reflects from it. The amount of energy reflected and transmitted through any discontinuity can expressed as reflection and transmission coefficients. In the literature different application for these coefficients may be found – the most often cited application is connected with localising changes in the geometry of structures. Changes in the coefficients due to cross section variations in rods and beams or due to existence of stiffeners in plates are well documented. However there are no application of using the reflection and transmission coefficients for damage size identification. For this reason the analysis presented in this paper has been carried out. The article presents a method of damage identification in 1D elements based on the wave propagation phenomenon and changes in reflection and transmission coefficients. The changes in transmission and reflection coefficients for waves propagating in isotropic rods with different types of damage have been analysed. The rods have been modelled with the elementary, two and three mode theories or rods. For numerical modelling the Spectral Finite Element Method has been used. Several examples are given in the paper.

The Wave Propagation through the Imperfect Interface between Two Micropolar Solids

2013 ◽  
Vol 803 ◽  
pp. 419-422 ◽  
Author(s):  
Chong Fu ◽  
Pei Jun Wei
Keyword(s):  
Wave Propagation ◽  
Boundary Conditions ◽  
Algebraic Equation ◽  
Linear Algebraic Equation ◽  
Imperfect Interface ◽  
Transmission Problem ◽  
Transverse Displacement ◽  
Reflection And Transmission ◽  
Transmission Coefficients ◽  
Rotational Waves

in this paper, the reflection and transmission problem of the coupled transverse displacement and transverse rotational waves at the imperfect interface between two different micropolar solids are studied. First, the boundary conditions between two micropolar solids with imperfect interface are used to derive the linear algebraic equation sets. Then, the linear algebraic equation sets are solved numerically and the results are shown graphically. Finally, the influence of the interface parameter reflecting the imperfect degree of interface on the reflection and the transmission coefficients are discussed based on the numerical results.Keyword: reflection and transmission, imperfect interface, micropolar solid, coupled waves.

Reflection and Refraction of Waves at a Planar Composite Interface

2011 ◽  
Author(s):  
Dale Chimenti ◽  
Stanislav Rokhlin ◽  
Peter Nagy
Keyword(s):  
Wave Propagation ◽  
Composite Materials ◽  
Boundary Conditions ◽  
Practical Importance ◽  
Ultrasonic Waves ◽  
Plane Interface ◽  
Contact Method ◽  
Reflection And Transmission ◽  
Transmission Coefficients ◽  
Composite Interface

Nondestructive ultrasonic testing of composite materials is affected by several special features of wave propagation that arise from the strong anisotropy and inhomogeneity of these materials. The resulting complexity requires re-examination of old testing methodologies and development of new ones. One of the most fundamental phenomena in ultrasonic nondestructive evaluation is the reflection–refraction of ultrasonic waves at a plane interface. Even the simplest test procedure requires understanding of mode conversion and knowledge of elastic wave reflection and transmission coefficients and refraction angles. Reflection–refraction phenomena, while straightforward and well documented for isotropic materials, are much more complicated for anisotropic materials. When analyzing the oblique incidence inspection method for composite materials, one first has to address the problem of wave propagation through the interface between the coupling medium and the composite material. For example, there is an inherent fluid/composite interface in the immersion technique and a perspex/composite interface in the contact method. In the latter case, assuming that a thin fluid layer is applied to facilitate coupling through the interface, slip rather than welded boundary conditions prevail. Another example of great practical importance is the case of multidirectional fiber plies in a composite laminate, when the reflection and transmission of ultrasonic waves from one ply to another with a different orientation must be considered. Before discussing the general problem of wave refraction in anisotropic composite materials, let us review the simple isotropic case. Consider a plane interface between two isotropic elastic media in “welded” (perfectly bonded) contact, implying continuity of tractions and displacements across the interface, although the boundary conditions are not important at this point. Figure 4.1 shows a schematic diagram of a plane wave with wavenumber ki incident on the interface at angle θi. The parallel lines with spacing equal to the incident wavelength λi correspond to equal-phase planes orthogonal to the incident plane. By definition, the wavenumber ki = 2π/λi is the magnitude of the wave vector ki. The incident wave is converted at the interface into reflected and transmitted waves. The refraction angle of the transmitted wave is θr and its wavenumber is kr.

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