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.

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.

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.

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

scholarly journals Buckling of regular, chiral and hierarchical honeycombs under a general macroscopic stress state

2014 ◽  
Vol 470 (2167) ◽  
pp. 20130856 ◽  
Author(s):  
Babak Haghpanah ◽  
Jim Papadopoulos ◽  
Davood Mousanezhad ◽  
Hamid Nayeb-Hashemi ◽  
Ashkan Vaziri
Keyword(s):  
Finite Element ◽  
Stress State ◽  
Closed Form ◽  
Plane Stress ◽  
Plane Stress State ◽  
Cellular Structures ◽  
Two Dimensional ◽  
Buckling Strength ◽  
Macroscopic Stress ◽  
Unit Cells

An approach to obtain analytical closed-form expressions for the macroscopic ‘buckling strength’ of various two-dimensional cellular structures is presented. The method is based on classical beam-column end-moment behaviour expressed in a matrix form. It is applied to sample honeycombs with square, triangular and hexagonal unit cells to determine their buckling strength under a general macroscopic in-plane stress state. The results were verified using finite-element Eigenvalue analysis.

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

The aerodynamic theory of sails. I. Two-dimensional sails

1961 ◽  
Vol 261 (1306) ◽  
pp. 402-422 ◽  
Keyword(s):  
Lift Coefficient ◽  
Linear Equations ◽  
Three Dimensional ◽  
Angle Of Incidence ◽  
Two Dimensional ◽  
Inviscid Incompressible Fluid ◽  
Two Dimensional Flow ◽  
Linearized Theory ◽  
High Degree ◽  
Additional Equation

This paper deals with the preliminaries essential for any theoretical investigation of three-dimensional sails—namely, with the two-dimensional flow of inviscid incompressible fluid past an infinitely-long flexible inelastic membrane. If the distance between the luff and the leach of the two-dimensional sail is c , and if the length of the material of the sail between luff and leach is ( c + l ), then the problem is to determine the flow when the angle of incidence α between the chord of the sail and the wind, and the ratio l / c are both prescribed; especially, we need to know the shape of, the loading on, and the tension in, the sail. The aerodynamic theory follows the lines of the conventional linearized theory of rigid aerofoils; but in the case of a sail, there is an additional equation to be satisfied which ex­presses the static equilibrium of each element of the sail. The resulting fundamental integral equation—the sail equation—is consequently quite different from those of aerofoil theory, and it is not susceptible to established methods of solution. The most striking result is the theoretical possibility of more than one shape of sail for given values of α and l / c ; but there appears to be no difficulty in choosing the shape which occurs in reality. The simplest result for these realistic shapes is that the lift coefficient of a sail exceeds that of a rigid flat plate (for which l / c = 0) by an amount approximately equal to 0.636 ( l / c ) ½ . It seems very doubtful whether analytical solutions of the sail equation will be found, but a method is developed in this paper which comes to the next best thing; namely, an explicit expression, as a matrix quotient, which gives numerical values to a high degree of accuracy at so many chord-wise points. The method should have wide application to other types of linear equations.

Feasibility of transient elastography versus real-time two-dimensional shear wave elastography in difficult-to-scan patients

2016 ◽  
Vol 51 (11) ◽  
pp. 1354-1359 ◽  
Author(s):  
Benjamin Staugaard ◽  
Peer Brehm Christensen ◽  
Belinda Mössner ◽  
Janne Fuglsang Hansen ◽  
Bjørn Stæhr Madsen ◽  
...  
Keyword(s):  
Real Time ◽  
Shear Wave ◽  
Transient Elastography ◽  
Shear Wave Elastography ◽  
Two Dimensional
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