Propagation at Short Ranges of Elastic Waves from an Impulsive Source in a Shallow Fluid Overlying a Layered Elastic Solid

1965 ◽  
Vol 37 (5) ◽  
pp. 894-898 ◽  
Author(s):  
A. S. Victor ◽  
F. R. Spitznogle ◽  
E. G. McLeroy
Keyword(s):  
Elastic Waves ◽  
Elastic Solid ◽  
Impulsive Source

scholarly journals Diffraction of plane elastic waves by a crack, with application to a problem of brittle fracture

1963 ◽  
Vol 3 (3) ◽  
pp. 325-339 ◽  
Author(s):  
M. Papadopoulos
Keyword(s):  
Elastic Waves ◽  
Scattered Field ◽  
Velocity Potential ◽  
Elastic Solid ◽  
Step Function ◽  
Free Surface Waves ◽  
Dependent Variables ◽  
Smooth Plane ◽  
New Feature ◽  
Set Up

AbstractA crack is assumed to be the union of two smooth plane surfaces of which various parts may be in contact, while the remainder will not. Such a crack in an isotropic elastic solid is an obstacle to the propagation of plane pulses of the scalar and vector velocity potential so that both reflected and diffracted fields will be set up. In spite of the non-linearity which is present because the state of the crack, and hence the conditions to be applied at the surfaces, is a function of the dependent variables, it is possible to separate incident step-function pulses into either those of a tensile or a compressive nature and the associated scattered field may then be calculated. One new feature which arises is that following the arrival of a tensile field which tends to open up the crack there is necessarily a scattered field which causes the crack to close itself with the velocity of free surface waves.

Multiple scattering of plane harmonic elastic waves in an infinite solid by an arbitrary configuration of obstacles

1969 ◽  
Vol 66 (2) ◽  
pp. 469-480 ◽  
Author(s):  
P. J. Barratt
Keyword(s):  
Scattering Amplitudes ◽  
Integral Equations ◽  
Multiple Scattering ◽  
Elastic Waves ◽  
Iterative Procedure ◽  
Elastic Solid ◽  
Single Scattering ◽  
Far Field ◽  
Rigid Spheres ◽  
Arbitrary Configuration

AbstractThe multiple scattering of plane harmonic P and S waves in an infinite elastic solid by arbitrary configurations of obstacles is considered. Integral equations relating the far-field multiple scattering amplitudes to the corresponding single scattering functions are obtained and asymptotic solutions are found by an iterative procedure. The scattering of a plane harmonic P wave by two identical rigid spheres is investigated.

scholarly journals Diffraction of Elastic Waves in Fluid-Layered Solid Interfaces by an Integral Formulation

2013 ◽  
Vol 2013 ◽  
pp. 1-9 ◽  
Author(s):  
J. E. Basaldúa-Sánchez ◽  
D. Samayoa-Ochoa ◽  
J. E. Rodríguez-Sánchez ◽  
A. Rodríguez-Castellanos ◽  
M. Carbajal-Romero
Keyword(s):  
Elastic Waves ◽  
Single Layer ◽  
Elastic Solid ◽  
Boundary Integral ◽  
Wave Number ◽  
Intermediate Step ◽  
Solid Models ◽  
Time Domains ◽  
Scattering Of Elastic Waves ◽  
Layered Solid

In the present communication, scattering of elastic waves in fluid-layered solid interfaces is studied. The indirect boundary element method is used to deal with this wave propagation phenomenon in 2D fluid-layered solid models. The source is represented by Hankel’s function of second kind and this is always applied in the fluid. Our method is an approximate boundary integral technique which is based upon an integral representation for scattered elastic waves using single-layer boundary sources. This approach is typically called indirect because the sources’ strengths are calculated as an intermediate step. In addition, this formulation is regarded as a realization of Huygens’ principle. The results are presented in frequency and time domains. Various aspects related to the different wave types that emerge from this kind of problems are emphasized. A near interface pulse generates changes in the pressure field and can be registered by receivers located in the fluid. In order to show the accuracy of our method, we validated the results with those obtained by the discrete wave number applied to a fluid-solid interface joining two half-spaces, one fluid and the other an elastic solid.

The motion excited by an impulsive source in an elastic half-space with a surface obstacle

1971 ◽  
Vol 61 (3) ◽  
pp. 747-763
Author(s):  
Jacob Aboudi
Keyword(s):  
Finite Difference ◽  
Perturbation Method ◽  
Half Space ◽  
Elastic Constants ◽  
Elastic Waves ◽  
Elastic Half Space ◽  
Reflected Waves ◽  
Finite Difference Solution ◽  
Impulsive Source ◽  
Difference Solution

abstract An elastic half-space having a surface obstacle of slightly different elastic constants whose deviation and shape of boundaries are small is considered. By combining a perturbation method and a finite difference solution, the motion of the half-space due to an impulsive source is given. Results show that Rayleigh and reflected waves are highly influenced by the existence of the obstacle and could give some indications for screening purposes of elastic waves.

Elastic Waves

2017 ◽  
Author(s):  
John A. Adam
Keyword(s):  
Elastic Waves ◽  
Small Amplitude ◽  
Equations Of Motion ◽  
Plane Waves ◽  
Elastic Solid ◽  
Stress And Strain ◽  
Field Equations ◽  
Strain Stress ◽  
Thermodynamic Variables ◽  
Dynamic Variables

This chapter focuses on the mathematics of elastic waves. In the case of a continuous medium, the field equations of physics (yielding the dynamic and thermodynamic variables) arise from three conservation equations: conservation of mass, momentum and energy. For an elastic medium, these equations of motion are known as Navier equations, which give rise to a rich variety of stress waves. There are two dynamic variables in an elastic solid: stress and strain. Stress and strain are linearly related in small-amplitude deformations; this relation is expressed by Hooke's law. The chapter first introduces the basic notation for elastic waves before discussing the solutions for plane waves. It also considers surface waves and Love waves.

Diffraction of elastic waves by a penny-shaped crack

1981 ◽  
Vol 378 (1773) ◽  
pp. 263-285 ◽  
Keyword(s):  
Integral Equation ◽  
Boundary Value Problem ◽  
Unique Solution ◽  
Double Layer ◽  
Elastic Waves ◽  
Boundary Value ◽  
Elastic Solid ◽  
Time Harmonic ◽  
Penny Shaped Crack ◽  
Shaped Crack

Consider an infinite elastic solid containing a penny-shaped crack. We suppose that time-harmonic elastic waves are incident on the crack and are required to determine the scattered displacement field u i . In this paper, we describe a new method for solving the corresponding linear boundary-value problem for u i , which we denote by S. We begin by defining an ‘elastic double layer’; we prove that any solution of S can be represented by an elastic double layer whose ‘density’ satisfies certain conditions. We then introduce various Green functions and define a new crack Green function, G ij , that is discontinuous across the crack. Next, we use G ij to derive a Fredholm integral equation of the second kind for the discontinuity in u i across the crack. We prove that this equation always has a unique solution. Hence, we are able to prove that the original boundary-value problem S always possesses a unique solution, and that this solution has an integral representation as an elastic double layer whose density solves an integral equation of the second kind.

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