Reflections, rays, and reverberations

1974 ◽  
Vol 64 (6) ◽  
pp. 1685-1696 ◽  
Author(s):  
B. L. N. Kennett
Keyword(s):  
Free Surface ◽  
Single Layer ◽  
Iterative Approach ◽  
Multilayered Media ◽  
Reflection And Transmission ◽  
Matrix Methods ◽  
Special Effects ◽  
Transmission Coefficients ◽  
Transmission Properties ◽  
Set Up

abstract The connection is established between conventional matrix methods for layered media and the reflection and transmission properties of a single layer. This interrelation is then used to set up an iterative approach to the calculation of reflection and transmission coefficients in multilayered media. This approach lends itself to a ray interpretation and allows estimates of errors involved in taking truncated partial ray expansions to be made. The special effects due to a free surface are also considered.

The acoustic signature for a surface-breaking crack produced by a point focus microscope

1992 ◽  
Vol 438 (1902) ◽  
pp. 47-65 ◽  
Keyword(s):  
Free Surface ◽  
Rayleigh Wave ◽  
Reflection And Transmission Coefficients ◽  
Reflection And Transmission ◽  
Acoustic Microscope ◽  
Transmission Coefficients ◽  
Acoustic Signature ◽  
Surface Breaking Crack ◽  
Line Focus ◽  
Fourier Integrals

The acoustic signature of a crack, breaking the surface of an otherwise homogeneous, isotropic elastic material, produced by a point focus scanning acoustic microscope is constructed theoretically. This work is patterned after a similar calculation carried out for the line focus microscope. The incident axisymmetric focused beam is constructed as a Fourier integral that produces a specified profile in the focal plane. The wavefields scattered from the specimen are also represented as Fourier integrals. Because the lens of the acoustic microscope is characterized by a large Fresnel number and an F number of order one, the Fourier integrals can be asymptotically approximated to obtain explicit expressions for the incident wavefield and for the wavefield scattered from a defect-free surface. The latter wavefield contains the leaky Rayleigh wave that is incident to the surface-breaking crack. The surface­-breaking crack is characterized by assigning it reflection and transmission coefficients. The wavefield scattered from the crack is estimated by tracing the leaky Rayleigh rays reflected and transmitted by the crack. The net wavefield scattered from the surface is then constructed by adding this crack scattered wavefield to that calculated for a defect-free surface. Lastly, the acoustic signature is calculated by using the appropriate incident and scattered wavefields in an electromechanical reciprocity identity that links the voltage measured at the microscope’s transducer to the scattered acoustic wavefields at the surface of the specimen. Expressions for acoustic signatures made using the line focus and point focus microscopes are compared. Moreover, from the expression for the acoustic signature, the Rayleigh wave reflection and transmission coefficients can be partly extracted.

Forced gravity waves in two-layered fluids with the upper fluid having a free surface

2003 ◽  
Vol 81 (4) ◽  
pp. 675-689 ◽  
Author(s):  
H H Sherief ◽  
M S Faltas ◽  
E I Saad
Keyword(s):  
Free Surface ◽  
Wave Motion ◽  
Harmonic Wave ◽  
Density Ratio ◽  
Finite Depth ◽  
Reflection And Transmission ◽  
Transmission Coefficients ◽  
Two Fluids ◽  
Lower Fluid ◽  
Wave Maker

The steady-gravity wave motion is considered for two immiscible layers of incompressible and nonviscous fluids in the presence of a porous wave maker immersed vertically in the two fluids, the upper fluid having a free surface and the lower fluid is of infinite depth. The boundary value problem for the velocity potentials is solved using Taylor's assumption on the wave maker. Also the scattering of a harmonic wave incident normally to the wave maker is considered and the reflection and transmission coefficients are obtained. The case when the lower fluid is of finite depth is also considered. The results are plotted for different values of porosity and different values of the density ratio. PACS Nos.: 47.35.+i, 47.55.Hd, 47.55.Mh

Manufacturability of Gmr Heads: 10Gb/in2 and Beyond

2000 ◽  
Vol 614 ◽  
Author(s):  
S. Sahu ◽  
Jian Chen ◽  
V. Talghader ◽  
S. Cool ◽  
S. Mao
Keyword(s):  
Process Control ◽  
Sheet Resistance ◽  
Spin Valve ◽  
Single Layer ◽  
Theoretical Understanding ◽  
Reflection And Transmission ◽  
Model Calculations ◽  
Transmission Coefficients ◽  
Synthetic Antiferromagnet ◽  
Strong Indicator

ABSTRACTConsistency of spin-valve stack deposition, both wafer-to-wafer and within a wafer, is key to the manufacturability of GMR heads. For typical GMR heads, film thicknesses are now in the range of 5Å-150Å and process control is becoming a challenge.This paper discusses the importance of characterizing the thickness and uniformity of each material in the spin-valve stack within the context of single layer sheet films. For this study, single layer sheet films and full multilayer spin-valve stacks were deposited in a multi-target cluster tool. The sheet resistance and thickness of the single layer sheet films were measured using a 4-point probe and ellipsometry, respectively. Results were then correlated to the sheet resistance and magnetic performance (i.e., GMR ratio, exchange field, and magneto-static coupling field) of the full spin-valve stacks with a synthetic antiferromagnet as the pinned layer. The 1σ < 2% uniformity, wafer-to-wafer and within wafer, realized for the full stacks is a strong indicator of a manufacturable process.Model calculations of the sheet resistance and GMR were carried out to provide theoretical understanding of the film thickness dependence. The calculated results are well correlated with the experimental measurements. The model is based on band structures and implicitly includes the momentum-dependent reflection and transmission coefficients at the interfaces.Results from both experiments and calculations show that process control and repeatability (both within a wafer and from wafer to wafer) are crucial to the spin-valve manufacturability, offering a critical challenge to the disc drive industry as it heads into the next generation of GMR heads.

Hydrodynamic characteristics of moored floating pipe breakwaters in random waves

2003 ◽  
Vol 217 (2) ◽  
pp. 95-110 ◽  
Author(s):  
V Sundar ◽  
R Sundaravadivelu ◽  
S Purushotham
Keyword(s):  
Hydrodynamic Performance ◽  
Hydrodynamic Characteristics ◽  
Random Waves ◽  
Mooring Lines ◽  
Reflection And Transmission ◽  
Transmission Coefficients ◽  
Motion Responses ◽  
Analysis Of Results ◽  
Mooring Forces ◽  
Set Up

The hydrodynamic performance characteristics of a floating pipe breakwater (FPBW) model (row of pipes separated by a distance equivalent to the pipe diameter) moored to the flume floor with slack moorings has been investigated in random waves through an experimental programme. The tests have been conducted on three models each with pipes of different diameter. The average reflection and transmission coefficients are evaluated from measurements and reported as a function of relative breakwater width. The motion responses, as well as the variations in the forces on the seaside and lee side mooring lines, are also presented. In addition, statistical analysis has been carried out to prove that the heave and surge motions, as well as the peak mooring forces, follow the Raleigh distribution. The details of the models, set-up, experimental procedure and analysis of results are presented and discussed.

scholarly journals Relaxed micromorphic modeling of the interface between a homogeneous solid and a band-gap metamaterial: New perspectives towards metastructural design

2017 ◽  
Vol 23 (12) ◽  
pp. 1485-1506 ◽  
Author(s):  
Angela Madeo ◽  
Gabriele Barbagallo ◽  
Manuel Collet ◽  
Marco Valerio d’Agostino ◽  
Marco Miniaci ◽  
...  
Keyword(s):  
Band Gap ◽  
Excellent Agreement ◽  
Continuum Model ◽  
Fem Simulation ◽  
Transmission Spectra ◽  
Reflection And Transmission ◽  
Indirect Measure ◽  
Material Parameters ◽  
Transmission Coefficients ◽  
Transmission Properties

In the present paper, the material parameters of the isotropic relaxed micromorphic model derived for a specific metamaterial in a previous contribution are used to model its transmission properties. Specifically, the reflection and transmission coefficients at an interface between a homogeneous solid and the chosen metamaterial are analyzed by using both the relaxed micromorphic model and a direct FEM implementation of the detailed microstructure. The obtained results show excellent agreement between the transmission spectra derived via our enriched continuum model and those issued by the direct FEM simulation. Such excellent agreement validates the indirect measure of the material parameters and opens the way towards an efficient metastructural design.

Reflection and Transmission of Rayleigh Surface Waves by a Material Interphase

1991 ◽  
Vol 58 (3) ◽  
pp. 688-694 ◽  
Author(s):  
Z. L. Li ◽  
J. D. Achenbach
Keyword(s):  
Free Surface ◽  
Boundary Element Method ◽  
Thin Layer ◽  
Surface Waves ◽  
Numerical Solutions ◽  
Singular Integral Equations ◽  
Mathematical Statement ◽  
Reflection And Transmission ◽  
Transmission Coefficients ◽  
Rayleigh Surface Waves

Reflection and transmission of Rayleigh surface waves by a juncture normal to the free surface, between identical or different materials, has been investigated. The juncture, which may be an interface containing defects or a thin layer, is represented by a layer of extensional and shear springs. The mathematical statement of the problem is reduced to a system of singular integral equations for the displacements on the free surface and the tractions and the displacements across the juncture. Numerical solutions of this system have been computed by the use of the boundary element method. Expressions for the reflection and transmission coefficients have subsequently been obtained by the use of half-plane Green’s functions in conjunction with an elastodynamic representation integral. Results are presented for selected values of the elastic constants of the joined bodies and the stiffness parameters of the juncture.

scholarly journals Reflection and transmission coefficients of a single layer in poroelastic media

2014 ◽  
Vol 135 (6) ◽  
pp. 3151-3162 ◽  
Author(s):  
Robiel Martinez Corredor ◽  
Juan E. Santos ◽  
Patricia M. Gauzellino ◽  
José M. Carcione
Keyword(s):  
Single Layer ◽  
Reflection And Transmission Coefficients ◽  
Reflection And Transmission ◽  
Transmission Coefficients ◽  
Poroelastic Media
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