On Waves in a Linear Elastic Half-Space with Free Boundary

2016 ◽  
Vol 52 (6) ◽  
pp. 587-598
Author(s):  
J. J. Rushchitsky
Keyword(s):  
Free Boundary ◽  
Half Space ◽  
Elastic Half Space ◽  
Linear Elastic

REFLECTION OF PLANE WAVES BY THE FREE BOUNDARY OF A POROUS ELASTIC HALF-SPACE

2003 ◽  
Vol 259 (2) ◽  
pp. 253-264 ◽  
Author(s):  
M. CIARLETTA ◽  
M.A. SUMBATYAN
Keyword(s):  
Free Boundary ◽  
Half Space ◽  
Plane Waves ◽  
Elastic Half Space

scholarly journals On a Certain Method of Selection of Domain for Finite Element Modelling of the Layered Elastic Half-Space in the Static Analysis of Flexible Pavement

2012 ◽  
Vol 58 (4) ◽  
pp. 477-501
Author(s):  
M. Nagórska
Keyword(s):  
Half Space ◽  
Mechanistic Model ◽  
Elastic Half Space ◽  
Original Method ◽  
Fe Model ◽  
Linear Elastic ◽  
Road Pavement ◽  
Viscoelastic Layers ◽  
Selection Of ◽  
Layered Half Space

AbstractIn the flexible road pavement design a mechanistic model of a multilayered half-space with linear elastic or viscoelastic layers is usually used for the pavement analysis.This paper describes a domain selection for the purpose of a FE model creating of the linear elastic layered half-space and boundary conditions on borders of that domain. This FE model should guarantee that the key components of displacements, stresses and strains obtained using ABAQUS program would be in particular identical with those ones obtained by analytical method using VEROAD program.It to achieve matching results with both methods is relatively easy for stresses and strains. However, for displacements, using FEM to obtain correct results is (understandably) highly problematic due to infinity of half-space. This paper proposes an original method of overcoming these difficulties.

ACOUSTIC EMISSION FROM PLASTIC SOURCES

2001 ◽  
Vol 09 (04) ◽  
pp. 1329-1345
Author(s):  
FRANZ ZIEGLER
Keyword(s):  
Acoustic Emission ◽  
Half Space ◽  
Plane Waves ◽  
Elastic Half Space ◽  
Small Scale ◽  
Line Load ◽  
Linear Elastic ◽  
Spherical Waves ◽  
Incremental Formulation ◽  
Observation Times

Monitoring of structures which may be subjected to overloads can be based on observing signals emitted in the course of developing defects. Ductile structures react on overloads by the formation of (small scale) plastic zones. Within the linear elastic background concept such an event is considered by the formation of sources of eigenstress. Since a direct description of the source characteristics is rather cumbersome we choose the time convolution of the imposed plastic strains with the complementary Green's stress dyadic to describe the signal of the acoustice mission. Thus, the dynamic generalization of Maysel's formula of thermo-elasticity, to include all kinds of eigenstrains, enters the field of computational acoustics. In that context, the novel contribution of this paper to acoustic emission and monitoring of (layered) structures is the formulation of the full 3-D problems and the introduction of the generalized rays in the background considering an instantaneous oblique force point source at the transducer's location. That means, all the information on the wave guide is contained in the Green's stress dyadic. The expansion into plane waves of cylindrical or spherical waves propagating in a layered elastic half-space or plate proves to be quite efficient for short observation times. Even the divergence effects of dipping interfaces of wedge-type layers are perfectly included by proper coordinate rotations and the exact "seismograms" are observed at a point receiver (where the localized plastic source is assumed to develop, commonly buried and often localized at an interface) from any source located at the hypo center (the site of the transducer in receiving mode, commonly placed at the "outer" surface). This nontrivial technique relies on the invariance of the phase function (arrival time) and of the infinitesimal amplitude of the plane waves in the ray expansion. The concept of the elastic background is illustrated by elastic-viscoplastic waves propagating in thin rods and subsequently extended to the 3-D problem of spherical waves with point symmetry. In that context and in an incremental formulation, the notion of plastic sources is introduced, which emit elastic waves in the background. Finally, the full 3-D problem in a layered half space or layered plate is solved in terms of generalized rays to be received at a transducer in receiving mode. Taking into account the progress in symbolic manipulation with integrated numeric capabilities (e.g., of Mathematica), such a formulation seems timely and may prove to be competitive to the entirely computational Finite Element Method of analysis of signals received from plastic sources. Time signatures of Green's displacement components at the surface of a half-space are illustrated when produced by a vertical, horizontal and inclined line load with a triangular time source function, respectively.

Reflection of Thermoelastic Waves From the Insulated Surface of a Solid Half-Space With Time-Delay

2020 ◽  
Vol 142 (9) ◽  
Author(s):  
Nihar Sarkar ◽  
Soumen De ◽  
Narayan Das ◽  
Nantu Sarkar
Keyword(s):  
Free Boundary ◽  
Half Space ◽  
Plane Waves ◽  
Generalized Thermoelasticity ◽  
Elastic Half Space ◽  
Reflection Coefficients ◽  
Angle Of Incidence ◽  
Energy Ratios ◽  
Thermally Conducting ◽  
Stress Free Boundary

Abstract This paper is devoted to study the reflection of thermoelastic plane waves from the thermally insulated stress-free boundary of a homogeneous, isotropic and thermally conducting elastic half-space. A new linear theory of generalized thermoelasticity under heat transfer with memory-dependent derivative (MDD) is employed to address this study. It has been found that three basic waves consisting of two sets of coupled longitudinal waves and one independent vertically shear-type wave may travel with distinct phase speeds. The formulae for various reflection coefficients and their respective energy ratios are determined in case of an incident coupled longitudinal elastic wave at the thermally insulated stress-free boundary of the medium. The results for the reflection coefficients and their respective energy ratios for various values of the angle of incidence are computed numerically and presented graphically for copper-like material and discussed.

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