Spherical wave scattering by an elastic solid cylinder of infinite length

1986 ◽  
Vol 79 (5) ◽  
pp. 1248-1259 ◽  
Author(s):  
Jean C. Piquette
Keyword(s):  
Wave Scattering ◽  
Spherical Wave ◽  
Elastic Solid ◽  
Infinite Length ◽  
Solid Cylinder

scholarly journals IV. On double refraction in a viscous fluid in motion

1874 ◽  
Vol 22 (148-155) ◽  
pp. 46-47 ◽  
Keyword(s):  
Internal Friction ◽  
Viscous Fluid ◽  
Polarized Light ◽  
Elastic Solid ◽  
The State ◽  
Solid Cylinder ◽  
Annular Space ◽  
Double Refraction ◽  
Fresh Start ◽  
The Moment

According to Poisson’s theory of the internal friction of fluids, a viscous fluid behaves as an elastic solid would do if it were periodically liquefied for an instant and solidified again, so that at each fresh start it becomes for the moment like an elastic solid free from strain. The state of strain of certain transparent bodies may be investigated by means of their action on polarized light. This action was observed by Brewster, and was shown by Fresnel to be an instance of double refraction. In 1866 I made some attempts to ascertain whether the state of strain in a viscous fluid in motion could be detected by its action on polarized light. I had a cylindrical box with a glass bottom. Within this box a solid cylinder could be made to rotate. The fluid to be examined was placed in the annular space between this cylinder and the sides of the box. Polarized light was thrown up through the fluid parallel to the axis, and the inner cylinder was then made to rotate. I was unable to obtain any result with solution of gum or sirup of sugar, though I observed an effect on polarized light when I compressed some Canada balsam which had become very thick and almost solid in a bottle.

ELASTODYNAMIC STRESS INTENSITY FACTOR FOR A FINITE CRACK IN ELASTIC SOLID UNDER 3D TRANSIENT LOADING OF MODE I

2013 ◽  
Vol 05 (04) ◽  
pp. 1350044
Author(s):  
XIANHONG MENG ◽  
ZHAOYU BAI ◽  
MING LI
Keyword(s):  
Stress Intensity Factor ◽  
Stress Intensity ◽  
Intensity Factor ◽  
Integral Transform ◽  
Elastic Solid ◽  
Scattered Wave ◽  
Mode I ◽  
Finite Width ◽  
Infinite Length ◽  
Distance Ratio

In this paper, the three-dimensional dynamic problem for an infinite elastic medium weakened by a crack of infinite length and finite width is analyzed, while the crack surfaces are subjected to mode I transient linear tractions. The integral transform approach is applied to reduce the governing differential equations to a pair of coupled singular integral equations, whose solutions can be obtained with the typical iteration method. The analytical solution of the stress intensity factor when the first wave and the first scattered wave reach the investigated crack tip is obtained. Numerical results are presented for different values of the width-to-longitudinal distance ratio z/l. It is found that the stress intensity factor decreases with the arrival of the first scattered longitudinal wave and increases with the arrival of the first scattered Rayleigh wave and tends to be stable. The static value considering both the first scattered wave and the first wave is about 50% greater than that considering only the first wave, and then the effect of the reflected wave is remarkable and deserves further study.

scholarly journals Lattice of infinite bending-resistant fibers

2016 ◽  
Vol 12 (2) ◽  
pp. 397-422
Author(s):  
Vladimir Kobelev
Keyword(s):  
Fracture Behavior ◽  
Hilbert Problem ◽  
Crack Tip ◽  
Elastic Solid ◽  
Periodic Lattice ◽  
Infinite Length ◽  
Two Dimensional ◽  
Content Type ◽  
Dimensional Lattice ◽  
Riemann Hilbert Problem

Purpose – The purpose of this paper is to introduce the double-periodic lattice, composed of bending-resistant fibers. The essence of the model is that the filaments are of infinite length and withstand tension and bending. The constitutive equations of the lattice in discrete and differential formulations are derived. Two complementary systems of loads, which cause different deformation two orthogonal families of fibers, occur in the lattice. The fracture behavior of the material containing a semi-infinite crack is investigated. The crack problem reduces to the exactly solvable Riemann-Hilbert problem. The solution demonstrates that the behavior of material cardinally depends upon the tension in the orthogonal family of fibers. If tension in fibers exists, opening of the crack under action of loads in two-dimensional lattice is similar to those in elastic solid. In the absence of tension, contrarily, there is a finite angle between edges at the crack tip. Design/methodology/approach – The description of stress state in the crack vicinity is reduced to the solution of mixed boundary value problem for simultaneous difference equations. In terms of Fourier images for unknown functions the problem is equivalent to a certain Riemann-Hilbert problem. Findings – The analytical solution of the problem shows that fracture behavior of the material depends upon the presence of stabilizing tension in fibers, parallel to crack direction. In the presence of tension in parallel fibers fracture character of two-dimensional lattice is similar to behavior of elastic solid. In this case the condition of crack grows can be formulated in terms of critical stress intensity factor. Otherwise, in the absence of stabilizing tension, the crack surfaces form a finite angle at the tip. Research limitations/implications – Linear behavior of fibers until rupture. Small deflections. Perfect two-dimensional lattice. Practical implications – The model provides exact analytical estimation of stresses on the crack tip as the function of fibers’ stiffness. Originality/value – The model is the extension of known lattice models, taking into account the semi-infinite crack in the lattice. This is the first known closed form solution for an infinite lattice model with the crack.

scholarly journals Mesoscale Acoustical Cylindrical Superlens

2018 ◽  
Vol 155 ◽  
pp. 01029 ◽  
Author(s):  
Igor Minin ◽  
Oleg Minin
Keyword(s):  
Wave Scattering ◽  
Near Field ◽  
Elastic Solid ◽  
Diffraction Limit ◽  
Solid Particles ◽  
Acoustic Metamaterials ◽  
Field Zone ◽  
Sharp Focusing ◽  
Plane Wave Scattering ◽  
First Time

We demonstrate experimentally for the first time the acoustojet (acoustic jets) formed from acoustic plane wave scattering by a penetrable cylindrical particle with dimensions of several wavelengths. It acts as a superlens with subwavelength localization of acoustical wave. During the scattering by elastic solid particles, additional internal shear waves are excited due to modes conversion. This mechanism allows achieving sharp focusing in the near-field zone. Such mesoscale single particle cylindrical lens may be considered as acoustic metamaterials free superlenses with resolution beyond the diffraction limit.

Surface Waves Guided by a Slit in an Elastic Solid

1972 ◽  
Vol 39 (4) ◽  
pp. 1027-1032 ◽  
Author(s):  
L. B. Freund
Keyword(s):  
Surface Waves ◽  
Crack Surface ◽  
Body Wave ◽  
Elastic Solid ◽  
Dispersion Relations ◽  
Finite Width ◽  
Infinite Length ◽  
Open Crack ◽  
Oblique Reflection ◽  
Rate Of Decay

Wave propagation in an isotropic elastic solid containing a slit is studied. The slit is viewed as an open crack of finite width and infinite length. In particular, the propagation of surface waves on the faces of the slit is considered. Making use of a reflection law for the oblique reflection of a Rayleigh wave from the tip of an open half-plane crack, surface waves are superimposed to form guided surface waves in the slit. In order to carry out the construction of dispersion relations, an assumption on the rate of decay of body wave modes localized in the vicinity of the edges of the guide is made, and the range of validity of the assumption is discussed. The dispersion relations are obtained by geometrical construction, and representative dispersion curves are shown.

Dilatational Spherical Wave Propagations of Multiple Energy Sources in Viscous Fluid-Saturated Elastic Porous Media

2012 ◽  
Author(s):  
Lu Han ◽  
Liming Dai
Keyword(s):  
Porous Media ◽  
Viscous Fluid ◽  
Spherical Wave ◽  
Elastic Solid ◽  
Stress Waves ◽  
Fluid Viscosity ◽  
Fundamental Theory ◽  
Compressible Viscous Fluid ◽  
Dissipation Term ◽  
Representative Model

Biot developed a representative model for the propagation of stress waves in a porous elastic solid containing a compressible viscous fluid, which is the fundamental theory about wave propagation in porous media. The solution proposed in that work has the same form under the model with or without fluid viscosity, though it is conflicted with the energy dissipation when the viscosity of flow is involved. In this study, the solution under the viscosity model has been modified with the exponential time dissipation term introduced to different forms under light and heavy viscosity, which complies with Biot’s oscillation form when there is no damping caused by fluid viscosity, and makes more sense as less oscillatory when the viscosity becomes large, as the energy will be dissipated in that case.

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