Waves at a Flexibly Bonded Interface

1967 ◽  
Vol 34 (4) ◽  
pp. 905-909 ◽  
Author(s):  
J. P. Jones ◽  
J. S. Whittier
Keyword(s):  
Frequency Equation ◽  
Wave Problem ◽  
Bond Behavior ◽  
Interface Waves ◽  
Rayleigh Surface Waves ◽  
Bonded Interface ◽  
Interface Wave ◽  
The Media ◽  
Limiting Case ◽  
Intermediate Bond

Plane strain-elastic wave propagation is studied for two dissimilar half spaces joined together at a plane interface by an elastic bond. The bond thickness is assumed to be small compared to the wavelength, and an appropriately simplified description of the bond behavior is introduced. Attention is focused on solutions corresponding to the propagation of interface waves along the bond. The existence of interface waves is found to be governed by a parameter involving bond stiffness and wavelength. The limiting case of an infinitely stiff bond corresponds to the interface wave problem first solved by Stoneley, and it is shown that the present analysis yields Stoneley’s frequency equation in this limit. Also, the limiting case of an infinitely soft bond is found as expected to give two Rayleigh surface waves, one in each medium. It is shown analytically that, for intermediate bond stiffnesses, there may occur zero, one, or two interface waves, depending on the properties of the bond and the media. Illustrative numerical examples are presented. It is the conclusion of this study that account must be taken of the stiffness of the bond and the wavelength of the disturbance before it is proper to speak of an interface wave existing or not existing at a bonded interface.

scholarly journals Propagation of leaking interface waves

1961 ◽  
Vol 51 (4) ◽  
pp. 527-555
Author(s):  
Robert A. Phinney
Keyword(s):  
P Wave ◽  
Transient Signal ◽  
New Wave ◽  
Wave Problem ◽  
Interface Waves ◽  
Solid Interface ◽  
Interface Wave ◽  
Physical Importance ◽  
Single Integral ◽  
Simple Interface

Abstract With simple generalizations of the method due to Rosenbaum (1961) and Phinney (1961), single integral expressions may be written down for the long range pole contributions to the transient signal in a plane seismic waveguide. This method yields expressions for the leaking, or imperfectly trapped waves, and suffers from no restriction on the number of layers or the existence of coupling to one or two half-spaces. When it is applied to the simple interface wave problem of two halfspaces in contact, closed form expressions are obtained describing the propagation of pulses along the interface due to lower sheet poles. The theory is applied to the Lamb problem, the liquid/solid interface, and the solid/solid interface problems. The leaking wave generalizations of the Rayleigh and Stoneley waves are found and a new wave, coupled to the P-wave, is demonstrated. The physical importance of leaking interface pulses is shown to be in their coupling to the normal or leaking oscillations of layered structures.

Cartesian Fingerprints in Beckett's Imagination Dead Imagine

2012 ◽  
Vol 21 (2) ◽  
pp. 223-243
Author(s):  
Irit Degani-Raz
Keyword(s):  
The Self ◽  
Levels Of Abstraction ◽  
The Media ◽  
The Mind ◽  
Limiting Case

The idea that Beckett investigates in his works the limits of the media he uses has been widely discussed. In this article I examine the fiction Imagination Dead Imagine as a limiting case in Beckett's exploration of limits at large and the limits of the media he uses in particular. Imagination Dead Imagine is shown to be the self-reflexive act of an artist who imaginatively explores the limits of that ultimate medium – the artist's imagination itself. My central aim is to show that various types of structural homologies (at several levels of abstraction) can be discerned between this poetic exploration of the limits of imagination and Cartesian thought. The homologies indicated here transcend what might be termed as ‘Cartesian typical topics’ (such as the mind-body dualism, the cogito, rationalism versus empiricism, etc.). The most important homologies that are indicated here are those existing between the role of imagination in Descartes' thought - an issue that until only a few decades ago was quite neglected, even by Cartesian scholars - and Beckett's perception of imagination. I suggest the use of these homologies as a tool for tracing possible sources of inspiration for Beckett's Imagination Dead Imagine.

scholarly journals On the Existence of Hydromagnetic Interface Waves at a Structured Atmosphere

1990 ◽  
Vol 142 ◽  
pp. 262-263
Author(s):  
K. Somasundaram ◽  
S. Manthiramoorthi ◽  
A. Sathya Narayanan
Keyword(s):  
Phase Velocity ◽  
Interface Waves ◽  
Photospheric Level ◽  
Interface Wave

The conditions under which the hydromagnetic interface waves can exist at a magnetic interface is deduced. Using these conditons, it is shown that a slow interface wave with a phase velocity about 5Km/s and a fast interface wave with a phase velocity 6.5 to 8km/s at the photospheric level can exist.

On waves at an interface between two liquids

1980 ◽  
Vol 88 (1) ◽  
pp. 183-191 ◽  
Author(s):  
P. F. Rhodes-Robinson
Keyword(s):  
Surface Wave ◽  
Interfacial Tension ◽  
Potential Flow ◽  
Wave Problem ◽  
Lower Region ◽  
Interface Wave ◽  
Wave Problems ◽  
Hydrodynamical Problem

AbstractIn this paper it is shown that a class of linearized interface-wave problems for two superposed inviscid liquids of unequal densities occupying regions which are symmetric about the interface can be reduced to a surface-wave problem in the lower region together with a classical hydrodynamical problem for potential flow in the lower region under a plane lid. The effect of interfacial tension is included. Examples of fundamental singularities in two semi-infinite liquids are given.

scholarly journals Analytic results for roots of two irrational functions in elastic wave propagation

1998 ◽  
Vol 40 (1) ◽  
pp. 72-79 ◽  
Author(s):  
L. M. Brock
Keyword(s):  
Wave Propagation ◽  
Elastic Wave ◽  
Surface Waves ◽  
Elastic Wave Propagation ◽  
Interface Waves ◽  
Rayleigh Surface Waves ◽  
Standard Operations

AbstractThe velocities of Rayleigh surface waves and, when they exist, Stoneley interface waves can be obtained as the roots of two irrational functions. Here previous results are extended by using standard operations related to the Wiener-Hopf technique to provide expressions in quadrature for these roots.

scholarly journals Krauklis wave in a stack of alternating fluid-elastic layers

Geophysics ◽  
2011 ◽  
Vol 76 (6) ◽  
pp. N47-N53 ◽  
Author(s):  
Valeri A. Korneev
Keyword(s):  
Fluid Layer ◽  
Wave Mode ◽  
Dispersive Wave ◽  
Low Frequencies ◽  
Interface Waves ◽  
Wave Velocities ◽  
Interface Wave ◽  
Fracture Mapping ◽  
Elastic Layers ◽  
Second Wave

The Krauklis wave is a slow dispersive wave mode that propagates in a fluid layer bounded by elastic media. In a model of alternating fluid and elastic layers, two interface waves can exist at low frequencies: The first wave propagates mostly in the elastic layer and has little dispersion, while the second wave can have strong dispersion and propagates as a Krauklis wave for some parameter combinations. Analytical conditions predict appearance of the Krauklis wave for higher frequencies and low porosities. Interface-wave velocities depend on model porosity, which potentially can be used for fracture mapping.

Vibration and Stability of Circular Plates Under Partially Distributed or Concentrated Inplane Loads

1985 ◽  
Vol 52 (3) ◽  
pp. 549-552 ◽  
Author(s):  
Y. Narita
Keyword(s):  
General Solution ◽  
Natural Frequencies ◽  
Elastic Stability ◽  
Solution Procedure ◽  
Frequency Equation ◽  
Nonuniform Distribution ◽  
Circular Plates ◽  
Buckling Loads ◽  
Free Transverse Vibration ◽  
Limiting Case

A method is presented for analyzing the free transverse vibration and elastic stability of circular plates under nonuniform distribution of the inplane stresses. A general solution procedure is developed, and a frequency equation is derived for the case when a pair of loads are locally distributed in the plane along the edge. Numerical results are presented for natural frequencies and buckling loads of the plates, and the effect of the partial inplane loading is discussed. A limiting case for a concentrated inplane load is also considered.

Analysis of radial vibrations in thick walled hollow poroelastic cylinder in the framework of Biot’s extension theory

2018 ◽  
Vol 14 (5) ◽  
pp. 970-983 ◽  
Author(s):  
Rajitha Gurijala ◽  
Malla Reddy Perati
Keyword(s):  
Phase Velocity ◽  
Attenuation Coefficient ◽  
Shear Viscosity ◽  
Frequency Equation ◽  
Extension Theory ◽  
Biot’S Theory ◽  
Radial Vibrations ◽  
Biot's Theory ◽  
Content Type ◽  
Limiting Case

Purpose In this paper, wave propagation in a poroelastic thick-walled hollow cylinder is investigated in the framework of Biot’s extension theory. Biot’s theory of poroelasticity is valid for isotropic porous solids saturated with non-viscous fluid. The bulk and shear viscosities are not considered in the classical Biot’s theory. Biot’s extension theory takes all these into an account. Biot’s extension theory is applied here to investigate the radial vibrations in thick-walled hollow poroelastic cylinder. The paper aims to discuss these issues. Design/methodology/approach By considering the stress-free boundaries, the frequency equation is obtained in the presence of dissipation. Limiting case when the ratio between thickness and inner radius is very small is investigated numerically. In the limiting case, the asymptotic expansions of Bessel functions are employed so that frequency equation is separated into two parts which gives attenuation coefficient and phase velocity. If the shear viscosity is neglected, then the problem reduces to that of the classical Biot’s theory. Findings For the numerical purpose, the solids Berea sandstone and bone are used. The results are presented graphically. Originality/value Radial vibrations of thick-walled hollow poroelastic cylinder are investigated in the framework of Biot’s extension theory. Due to the mathematical complexity, limiting case is considered. The complex valued frequency equation is discussed numerically which gives the attenuation coefficient and phase velocity. If shear viscosity is neglected, then the problem reduces to that of the classical Biot’s theory. The comparison has been made between the current results and that of classical results.

scholarly journals Oblique interface-wave diffraction by a small bottom deformation in two superposed fluids

1996 ◽  
Vol 19 (2) ◽  
pp. 363-370 ◽  
Author(s):  
B. N. Mandal ◽  
U. Basu
Keyword(s):  
Integral Theorem ◽  
Interface Waves ◽  
First Order ◽  
Two Fluids ◽  
Transmission And Reflection Coefficients ◽  
Bottom Deformation ◽  
Interface Wave ◽  
Lower Fluid ◽  
Superposed Fluids ◽  
Transmission And Reflection

The problem of diffraction of oblique interface-waves by a small bottom deformation of the lower fluid in two superposed fluids has been investigated here assuming linear theory and invoking a simplified perturbation analysis. First order corrections to the velocity potentials in the two fluids are obtained by using the Green's integral theorem in a suitable manner. The transmission and reflection coefficients are evaluated approximately. These reduce to the known results for a single fluid in the absence of the upper fluid.

Prediction of the Wavelength of Interface Waves in Symmetric Explosive Welding

1976 ◽  
Vol 18 (2) ◽  
pp. 87-94 ◽  
Author(s):  
S. R. Reid ◽  
N. H. S. Sherif
Keyword(s):  
Vortex Shedding ◽  
Explosive Welding ◽  
Wave Formation ◽  
Fluid Stream ◽  
Rigorous Analysis ◽  
Interface Waves ◽  
First Approximation ◽  
Interface Wave ◽  
Semi Empirical ◽  
The Waves

A theory is developed for calculating the wavelength of the waves produced at the welded interface between two identical and explosively projected (flyer) plates using the so-called symmetric welding arrangement. The theory appeals to the analogy between interface wave formation and the formation of a vortex street behind an obstacle in a fluid stream which has been discussed elsewhere (1)‡. It is a notional theory in the sense that the results of an inviscid analysis of jet collision are combined with a semi-empirical vortex shedding theory. In spite of this, the authors believe that it provides a useful first approximation to a more rigorous analysis, and this belief is supported by the agreement found between the theory and certain experimental results obtained from the welding of steel flyer plates.

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