Shear Waves Guided by a Cylindrical Hole in a Finitely Deformed Elastic Solid

1972 ◽  
Vol 39 (3) ◽  
pp. 703-708 ◽  
Author(s):  
M. Kurashige
Keyword(s):  
Phase Velocity ◽  
Small Amplitude ◽  
Shear Waves ◽  
Elastic Solid ◽  
Cylindrical Hole ◽  
Initial Stresses ◽  
Axisymmetric Case ◽  
Infinite Extent ◽  
Cylindrical Bore ◽  
Basic Equations

The present paper deals with the propagation of unattenuated axisymmetric waves of small amplitude guided by a cylindrical bore through a neo-Hookean solid of infinite extent, which is finitely deformed by an all-around tension at infinity. The basic equations for the axisymmetric case are derived on the basis of Biot’s mechanics of incremental deformations, and applied to the problem by using Galerkin’s method. The influence of nonhomogeneous initial stresses upon the phase velocity of shear waves is presented in the form of curves.

Radial Propagation of Axial Shear Waves in a Finitely Deformed Elastic Solid

1974 ◽  
Vol 41 (1) ◽  
pp. 83-88 ◽  
Author(s):  
M. Kurashige
Keyword(s):  
Wave Propagation ◽  
Method Of Characteristics ◽  
Shear Waves ◽  
Elastic Solid ◽  
Radial Deformation ◽  
Numerical Examples ◽  
Axial Shear ◽  
Cylindrical Bore ◽  
Basic Equations ◽  
Radial Propagation

A study is made of the radial propagation of axial shear waves in an incompressible elastic solid under finite radial deformation. Basic equations are derived on the basis of Biot’s mechanics of incremental deformations, and analysis is made by the method of characteristics. Numerical examples are given by specializing the initial deformation to two cases: (a) an infinite solid with a cylindrical bore is inflated by all-around tension, and (b) a cuboid is rounded into a ring and its ends are bonded to each other. The influence of the inhomogeneities of such deformations upon the laws of shear wave propagation is presented in the form of curves.

Attenuation and dispersion phenomena of shear waves in anelastic and elastic porous strips

2021 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Parvez Alam ◽  
Suprava Jena ◽  
Irfan Anjum Badruddin ◽  
Tatagar Mohammad Yunus Khan ◽  
Sarfaraz Kamangar
Keyword(s):  
Shear Wave ◽  
Half Space ◽  
Special Functions ◽  
Shear Waves ◽  
Finite Thickness ◽  
Dissipation Factor ◽  
Initial Stresses ◽  
Whittaker Functions ◽  
Content Type ◽  
Attenuation And Dispersion

Purpose This paper aims to study the attenuation and dispersion phenomena of shear waves in anelastic and elastic porous strips. Numerical investigations are performed for the phase and damped velocity profiles of the wave. For numerical computation purposes, water-saturated limestone and kerosene oil saturated sandstone for the first and second porous strips, respectively. Some other peculiarities have been observed and discussed. Design/methodology/approach Dispersion and attenuation characteristic of the shear wave propagations have been studied in an inhomogeneous poro-anelastic strip of finite thickness, which is clamped between an inhomogeneous poroelastic strip of finite thickness and an elastic half-space. Both the strips are initially stressed and the half-space is self-weighted. Analytical methods are used to calculate the interior deformations of the model with the involvement of special functions. The determination of the frequency equation, which includes the Bessel’s and Whittaker functions, has been obtained using the prescribed boundary conditions. Findings Impacts of attenuation coefficient, dissipation factor, inhomogeneities, initial stresses, Biot’s gravity, porosity and thickness ratio parameters on the velocity profile of the wave have been demonstrated through the graphical visuals. These parameters are playing an important role and working as a catalyst in affecting the propagation behaviour of the wave. Originality/value Inclusion of the concept of doubly layered initially stressed inhomogeneous porous structure of elastic and anelastic medium bedded over a self-weighted half-space medium brings a novelty to the existing literature related to the study of shear wave. It may be helpful to geologists, seismologists and structural engineers in the development of theoretical and practical studies.

On the synthesis of shear-coupled PL waves

1968 ◽  
Vol 58 (6) ◽  
pp. 1849-1877 ◽  
Author(s):  
Ramesh Chander ◽  
L. E. Alsop ◽  
Jack Oliver
Keyword(s):  
United States ◽  
Phase Velocity ◽  
Travel Time ◽  
Current Knowledge ◽  
Shear Waves ◽  
The United States ◽  
Synthetic Seismograms ◽  
Travel Times ◽  
Precise Knowledge ◽  
S Curve

ABSTRACT Using the shear-coupled PL wave hypothesis of Oliver as a basis, a method is developed for computing synthetic long-period seismograms between the onset of the initial S-type body phase and the beginning of surface waves. Comparison of observed and synthetic siesmograms shows that this hypothesis can explain, in considerable detail, most of the waves with periods greater than about 20 sec recorded during this interval. The synthetic seismograms are computed easily on a small digital computer; they resemble the observed seismograms much more closely than the synthetic seismograms obtained through the superposition of normal modes of the Earth that have been reported in the literature. The synthesis of shear-coupled PL waves depends on a precise knowledge of the phase-velocity curve of the PL wave and travel-time curves of shear waves. Hence, in principle, if one of these quantities is well-known the other can be determined by this method. Phase-velocity curves of the PL wave are determined for the Baltic shield, the Russian platform, the Canadian shield, the United States, and the western North-Atlantic ocean, on the assumption that J-B travel-time curves of shear waves apply to these areas. These dispersion curves show the type of variations to be expected on the basis of the current knowledge of the crustal structures in these areas. Examples are presented to show that J-B travel-times of shear waves along paths between Kenai Peninsula, Alaska and Palisades, equatorial mid-Atlantic ridge and Palisades, and Kurile Islands and Uppsala need to be revised. Shear-wave travel-time curves that are not unique for reasons explained in the study but that give synthetic seismograms in agreement with the observed seismograms were obtained. The new S curves are compared with the J-B travel-time curves for S; and they all predict S waves to arrive later than the time given by J-B tables for epicentral distances smaller than about 30°. The new S curve for the Alaska to Palisades path appears to agree with one of the branches of a multi-branched S curve proposed recently by Ibrahim and Nuttli for the ‘average United States’ insofar as travel-times are concerned, but there are some differences in the slopes of the two curves.

scholarly journals Anti-plane shear waves in periodic elastic composites: band structure and anomalous wave refraction

2015 ◽  
Vol 471 (2180) ◽  
pp. 20150152 ◽  
Author(s):  
Sia Nemat-Nasser
Keyword(s):  
Band Structure ◽  
Phase Velocity ◽  
Negative Refraction ◽  
Mass Density ◽  
Shear Waves ◽  
Variable Mass ◽  
Three Dimensional ◽  
Positive Energy ◽  
Plane Shear ◽  
Elastic Composites

For anti-plane shear waves in periodic elastic composites, it is shown that negative energy refraction can be accompanied by positive phase-velocity refraction and positive energy refraction can be accompanied by negative phase-velocity refraction , and that this can happen over a broad range of frequencies. Hence, in general, negative refraction does not necessarily require antiparallel group and phase-velocity vectors. Details are given for layered composites and the results are extended to, and illustrated for, two-dimensional periodic composites, revealing a wealth of information about the refractive characteristics of this class of composites. The composite's unit cell may consist of any number of constituents of any variable mass density and elastic modulus, admitting large discontinuities . A powerful variational-based solution method is used that applies to one-, two- and three-dimensional composites, irrespective of their constituents being homogeneous or heterogeneous. The calculations are direct, accurate and efficient, yielding the band structure, group-velocity, energy-flux and phase-velocity vectors as functions of the frequency and wavevector components, over an entire frequency band.

The Horizontally Polarized Shear Waves in Multilayered Piezo-Composites with 2-2 Connectivity

2004 ◽  
Vol 261-263 ◽  
pp. 465-470
Author(s):  
Zheng Hua Qian ◽  
Feng Jin ◽  
Zi Kun Wang ◽  
Kikuo Kishimoto
Keyword(s):  
Thin Film ◽  
Thin Films ◽  
Phase Velocity ◽  
Polymer Composites ◽  
Piezoelectric Ceramic ◽  
Shear Waves ◽  
Electrical Performance ◽  
Sh Waves ◽  
Structural Applications ◽  
Waves Propagation

Following the advances in structural applications, composite structures are being used commonly in transducer applications to improve acoustic, mechanical and electrical performance of piezoelectric devices. Functional composite transducers for sensors and actuators generally consist of ceramics and polymers, the disadvantage of the brittleness nature of the piezoelectric ceramics can be overcome and the structures especially good for sensing can be allowed for building up. Propagation behavior of horizontally polarized shear waves (SH-waves) in piezoelectric ceramic-polymer composites with 2-2 connectivity is taken into account. The multilayer structures are consisted of piezoelectric thin films bonded perfectly with polymeric thin films alternately. The phase velocity equations of SH-waves propagation in the piezoelectric ceramic-polymer composites with 2-2 connectivity are obtained for the cases of wave propagation in the direction perpendicular to the layering and along the layering, respectively. Filter effect of this kind of structure and the effect of volume fraction and shear modulus ratio of piezoelectric layer to polymer layer on the phase velocity are discussed in detail, respectively. One practical combination of piezoelectric thin film-polymer thin film multilayer system is chosen to carry out the numerical simulation, some basic properties of SH-waves propagation in above multilayered structures are revealed.

scholarly journals SOLUTION OF PRIVATE TASKS OF CYLINDRICAL SHEAR WAVES (in the case of the distribution of constant values γ-α + 2> 0 and α = β)

2020 ◽  
Vol 6 (334) ◽  
pp. 19-26
Author(s):  
A. Seitmuratov ◽  
◽  
M.Zh. Aitimov ◽  
A. Seitkhanova ◽  
A. Ostayeva ◽  
...  
Keyword(s):  
Fixed Point ◽  
Phase Velocity ◽  
Rheological Properties ◽  
Shear Waves ◽  
The Body ◽  
Rheological Parameters ◽  
Vibration Frequencies ◽  
Complex Phase ◽  
Wave Characteristics ◽  
Fixed Moment

Many studies usually use two methods to determine wave characteristics. First-The instantaneous state of the medium corresponding to a certain fixed moment of time is investigated. Second-The change in time of the state of the body in question at some fixed point is investigated. If studies are carried out taking into account the rheological properties of the material of the system in question or, if there is an environment surrounding the system, which also generally exhibits rheological properties, the use of these methods is significantly difficult. In such cases, the influence of rheological parameters on the components of the complex phase velocity at certain values of the vibration frequencies is studied.

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