Reflection of Flexural Waves at the Edge of a Plate

1954 ◽  
Vol 21 (3) ◽  
pp. 213-220
Author(s):  
T. R. Kane
Keyword(s):  
Shear Wave ◽  
Plate Theory ◽  
Infinite Plate ◽  
Flexural Wave ◽  
Angle Of Incidence ◽  
Two Dimensional ◽  
Flexural Waves ◽  
Arbitrary Angle ◽  
Reflected Waves ◽  
Special Cases

Abstract The reflection of straight-crested flexural waves at the edge of a semi-infinite plate is studied in terms of a two-dimensional plate theory. It is found that, in general, a flexural wave propagated toward the edge at an arbitrary angle of incidence gives rise to three reflected waves: two flexural waves and a shear wave. A number of special cases, involving degenerate forms of these motions, are investigated in detail.

Reflection of Dilatational Waves at the Edge of a Plate

1957 ◽  
Vol 24 (2) ◽  
pp. 219-227
Author(s):  
T. R. Kane
Keyword(s):  
Shear Wave ◽  
Plane Stress ◽  
Plate Theory ◽  
Angle Of Incidence ◽  
Two Dimensional ◽  
Arbitrary Angle ◽  
Reflected Waves ◽  
Dilatational Wave ◽  
Special Cases

Abstract The reflection of straight-crested dilatational waves at the edge of a semi-inflnite plate is studied in terms of a two-dimensional plate theory and in terms of the theory of generalized plane stress. It is found that, in general, a dilatational wave propagated toward the edge at an arbitrary angle of incidence gives rise to three reflected waves; namely, two dilatational waves and a shear wave. A number of special cases are investigated in detail.

scholarly journals Fundamental problems for infinite plate with a curvilinear hole having finite poles

2001 ◽  
Vol 7 (6) ◽  
pp. 485-501 ◽  
Author(s):  
M. A. Abdou ◽  
A. A. El-Bary
Keyword(s):  
Complex Variable ◽  
Arbitrary Shape ◽  
Infinite Plate ◽  
Mapping Function ◽  
Curvilinear Hole ◽  
Two Dimensional ◽  
Rational Mapping ◽  
Special Cases ◽  
Elasticity Problems ◽  
Different Shapes

In the present paper Muskhelishvili's complex variable method of solving two-dimensional elasticity problems has been applied to derive exact expressions for Gaursat's functions for the first and second fundamental problems of the infinite plate weakened by a hole having many poles and arbitrary shape which is conformally mapped on the domain outside a unit circle by means of general rational mapping function. Some applications are investigated. The interesting cases when the shape of the hole takes different shapes are included as special cases.

MHD stagnation-point flows at a current sheet including viscous and resistive effects: general two-dimensional solutions

1990 ◽  
Vol 44 (3) ◽  
pp. 525-546 ◽  
Author(s):  
T. D. Phan ◽  
B. U. Ö. Sonnerup
Keyword(s):  
Magnetic Field ◽  
Reynolds Number ◽  
Current Sheet ◽  
Stagnation Point ◽  
Angle Of Incidence ◽  
Two Dimensional ◽  
Viscous Effects ◽  
Special Cases ◽  
The Magnetic Field ◽  
A Current

Exact solutions are presented of two-dimensional steady-state incompressible stagnation point flows at a current sheet separating two colliding plasmas. They describe the process of resistive field annihilation (zero reconnection) where the magnetic field in each plasma is strictly parallel to the current sheet, but may have different magnitudes and direction on its two sides. The flow in the (x, y) plane toward the current sheet, located at x = 0, may have an arbitrary angle of incidence and an arbitrary amount of divergence from or convergence towards the stagnation point. We find the most general form of the solution for the plasma velocity and for the magnetic field. For the z compenents of the flow and field, solutions in the form of truncating power series in y are found. The cases obtained in this study contain the solutions obtained by Parker, Sonnerup & Priest, Gratton et al. and Besser, Biernat & Rijnbeek as special cases. The role of viscosity in determining the flow and field configurations is examined. When the two colliding plasmas have the same viscosity and density, it is shown that viscous effects usually are important only in strongly divergent or convergent viscous flows with viscous Reynolds number of the order of unity or smaller. For astrophysical applications the viscous Reynolds number is usually high and the effects of viscosity on the interaction of plasmas of similar properties are small. The formulation of the stagnation-point flow problem involving plasmas of different properties is also presented. Sample cases of such flows are shown. Finally, a possible application of the results from this study to the earth's magnetopause is discussed briefly.

Stress Intensity Factors for Plate Bending and Shearing Problems

1994 ◽  
Vol 61 (3) ◽  
pp. 719-722 ◽  
Author(s):  
A. T. Zehnder ◽  
Chung-Yuen Hui
Keyword(s):  
Stress Intensity ◽  
Stress Intensity Factors ◽  
Plate Theory ◽  
Infinite Plate ◽  
Bending Moment ◽  
Far Field ◽  
Intensity Factors ◽  
Arbitrary Angle ◽  
Cracked Plate ◽  
Finite Crack

Stress intensity factors for a finite crack in an infinite plate are calculated assuming Kirchhoff plate theory. Two problems are considered: a cracked plate subjected to uniform far-field shearing, and a cracked plate subjected to uniform far-field bending moment. In both cases the crack is oriented at an arbitrary angle to the axis of loading.

Noninvasive Assessment of Liver Diseases using 2D Shear Wave Elastography

2016 ◽  
Vol 25 (4) ◽  
pp. 525-532 ◽  
Author(s):  
Monica Lupșor-Platon ◽  
Radu Badea ◽  
Mirela Gersak ◽  
Anca Maniu ◽  
Ioana Rusu ◽  
...  
Keyword(s):  
Shear Wave ◽  
Predictive Value ◽  
Liver Diseases ◽  
Venous Pressure ◽  
Liver Stiffness ◽  
Shear Wave Elastography ◽  
Acoustic Radiation Force Impulse ◽  
Two Dimensional ◽  
Non Invasive ◽  
Examination Technique

There has been great interest in the development of non-invasive techniques for the diagnosis of liver fibrosis in chronic liver diseases, including ultrasound elastographic methods. Some of these methods have already been adequately studied for the non-invasive assessment of diffuse liver diseases. Others, however, such as two-dimensional Shear Wave Elastography (SWE), of more recent appearance, have yet to be validated and some aspects are for the moment incompletely elucidated. This review discusses some of the aspects related to two-dimensional SWE: the examination technique, the examination performance indicators, intra and interobserver agreement and clinical applications. Recommendations for a high-quality examination technique are formulated. Key words:  –  –  – Two-dimensional Shear Wave Elastography. Abbreviations: 2D- SWE: Two-dimensional Shear Wave Elastography; 3D- SWE: Three-dimensional Shear Wave Elastography; AUROC: area under the receiver operating characteristic curves; ARFI Acoustic Radiation Force Impulse Elastography; EFSUMB: European Federation of Societies for Ultrasound in Medicine and Biology; HVPG: hepatic venous pressure gradient; LS: liver stiffness; LR: likelihood ratio; NPV: negative predictive value; PPV: positive predictive value; ROI: region of interest; RT-E: Real Time-Elastography; Se: sensitivity; Sp: specificity; TE: Transient Elastography; US: ultrasound; VM: valid measurement; E: Young’s modulus

Fast and slow interaction of elastic waves with platonic clusters

2011 ◽  
Vol 467 (2136) ◽  
pp. 3509-3529 ◽  
Author(s):  
Michael H. Meylan ◽  
Ross C. McPhedran
Keyword(s):  
Elastic Waves ◽  
Early Time ◽  
Approximate Solutions ◽  
Wave Profile ◽  
Flexural Wave ◽  
Flexural Waves ◽  
Analytical Extension ◽  
Scattering Of Elastic Waves ◽  
Classical Models ◽  
The Time Domain

We study the scattering of elastic waves by platonic clusters in the time domain, both for plane wave excitations and for a specified initial wave profile. We show that we can use an analytical extension of our problem to calculate scattering frequencies of the solution. These allow us to calculate approximate solutions that give the flexural wave profile accurately in and around the cluster for large times. We also discuss the early-time behaviour of flexural waves in terms of the classical models of Sommerfeld and Brillouin.

Performance of two--dimensional ultrasound shear wave elastography: reference values of normal liver stiffness in children

2018 ◽  
Vol 49 (1) ◽  
pp. 91-98 ◽  
Author(s):  
Paraskevi Galina ◽  
Efthymia Alexopoulou ◽  
Aglaia Zellos ◽  
Virginia Grigoraki ◽  
Tania Siahanidou ◽  
...  
Keyword(s):  
Shear Wave ◽  
Reference Values ◽  
Liver Stiffness ◽  
Shear Wave Elastography ◽  
Normal Liver ◽  
Two Dimensional

scholarly journals Two-dimensional Shear-Wave Elastography and Conventional US: The Optimal Evaluation of Liver Fibrosis and Cirrhosis

Radiology ◽  
2015 ◽  
Vol 275 (1) ◽  
pp. 290-300 ◽  
Author(s):  
Jian Zheng ◽  
Huanyi Guo ◽  
Jie Zeng ◽  
Zeping Huang ◽  
Bowen Zheng ◽  
...  
Keyword(s):  
Liver Fibrosis ◽  
Shear Wave ◽  
Shear Wave Elastography ◽  
Two Dimensional ◽  
Optimal Evaluation
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