scholarly journals Numerically evaluated displacement and stress solutions for a 3D viscoelastic half space subjected to a vertical distributed surface stress loading using the Radon and Fourier transforms

2006 ◽  
Vol 23 (8) ◽  
pp. 787-804 ◽  
Author(s):  
Marco Adolph ◽  
Euclides Mesquita ◽  
Edson Rodrigues Carvalho ◽  
Edivaldo Romanini
Keyword(s):  
Half Space ◽  
Surface Stress ◽  
Fourier Transforms

scholarly journals Natural boundary conditions and nearsurface non-homogeneity in nonferromagnetic electro conductive half-space and layer

2017 ◽  
pp. 100-112
Author(s):  
Taras Nahirnyj ◽  
Kostiantyn Tchervinka
Keyword(s):  
Half Space ◽  
Surface Stress ◽  
Electric Double Layer ◽  
The Body ◽  
Physical Parameters ◽  
Solid Model ◽  
Force Load ◽  
Natural Boundary ◽  
Near Surface ◽  
Natural Boundary Conditions

Within the framework of the local nonhomogeneous electroconductive solid model the regularities of near surface non-homogeneity in half-space and layer are studied. Two characteristic sizes are inherent to this non-homogeneity. It is shown that in a free of force load body the values of surface stress and surface, charge are uniquely defined by physical parameters of the material and the body. The electric double layer is the result of taking into account the structural non-homogeneity of material and the forces of Coulomb interaction.

scholarly journals Structural Monitoring of Underground Structures in Multi-Layer Media by Dynamic Methods

Sensors ◽  
2020 ◽  
Vol 20 (18) ◽  
pp. 5241 ◽  
Author(s):  
Alexandr Lyapin ◽  
Alexey Beskopylny ◽  
Besarion Meskhi
Keyword(s):  
Half Space ◽  
Dynamic Load ◽  
Fourier Transforms ◽  
Sensor System ◽  
Structural Monitoring ◽  
Dynamic Features ◽  
Surface Source ◽  
Stress Strain ◽  
Dynamic Surface ◽  
Actual Problem

The actual problem of structural monitoring and modeling of dynamic response from buried building is considered in the framework of arbitrary dynamic load. The results can be used for designing underground transport constructions, crossings, buried reservoirs and foundations. In existing methods, the system of sensors that register the response to a dynamic action does not allow for effective interpretation of the signal without understanding the dynamic features and resonance phenomena. The analytical and numerical solution of the problem of the dynamics of a buried object in a layered medium is considered. A multilayer half-space is a set of rigidly interconnected layers characterized by elastic properties. At a distance, an arbitrary dynamic load acts on the half-space, which causes oscillations in the embedded structure, and the sensor system registers the response. The problem of assessing the dynamic stress-strain state (DSSS) is solved using Fourier transforms with the principle of limiting absorption. As an example, the behavior of an embedded massive structure of an underground pedestrian crossing under the influence of a dynamic surface source on a multilayer medium is considered, as well as instrumental support of the sensor system. The solution in the form of stress, strain and displacement fields is obtained and compared with the experimental data. The frequency-dependent characteristics of the system are determined and the possibility of determining the DSSS by a shock pulse is shown.

Impact and Moving Loads on a Slightly Curved Elastic Half Space

1959 ◽  
Vol 26 (4) ◽  
pp. 491-498
Author(s):  
A. C. Eringen ◽  
J. C. Samuels
Keyword(s):  
Half Space ◽  
Fourier Transforms ◽  
Normal Load ◽  
Elastic Half Space ◽  
Two Dimensional ◽  
Moving Loads ◽  
Special Cases ◽  
Indefinite Integral ◽  
Wavy Boundary ◽  
Boundary Curves

Abstract Two-dimensional Fourier transforms are employed to treat the two-dimensional dynamic problem of elastic half space having a slightly wavy boundary. The various boundary curves considered include square and triangular bumps and holes, and sinusoidal and periodic boundaries. The number of different types of surface loadings considered are: (a) Normal tractions and zero shear, (b) impulsive normal tractions and zero shear, (c) suddenly applied normal tractions and zero shear, (d) concentrated normal load and zero shear, (e) concentrated impulsive load and zero shear, (f) pulsating normal load and zero shear, (g) moving loads, (h) pulsating moving loads, (i) vertical and horizontal loads, (j) moving vertical loads. Stress and displacement components for special cases of the loads described in (a, c, f, and g) acting on a sinusoidal boundary lead to a solution which requires evaluation of a single indefinite integral. Closed-form results are given for a uniform pulsating pressure load.

Tempered Distributions Supported on a Half-Space of RN and Their Fourier Transforms

1991 ◽  
Vol 43 (1) ◽  
pp. 61-88
Author(s):  
Jean-Pierre Gabardo
Keyword(s):  
Fourier Transform ◽  
Fourier Analysis ◽  
Half Space ◽  
Fourier Transforms ◽  
Fundamental Problem ◽  
Half Line ◽  
Tempered Distributions ◽  
Difficult Question ◽  
Wiener Theorem ◽  
Special Cases

A fundamental problem in Fourier analysis is to characterize the behaviour of a function (or distribution) whose Fourier transform vanishes in some particular set. Of course, this is, in general, a very difficult question and little seems to be known, except in some special cases. For example, a theorem of Paley-Wiener (Theorem XII in [6]) characterizes exactly the behaviour of the modulus of a function in L2(R) whose Fourier transform vanishes on a half-line.

Response of ramp-type heating in a monoclinic generalized thermoelastic material

2020 ◽  
Vol 16 (6) ◽  
pp. 1373-1384
Author(s):  
Leena Rani ◽  
Sushant Shekhar
Keyword(s):  
Half Space ◽  
Thermal Loading ◽  
Fourier Transforms ◽  
Generalized Thermoelasticity ◽  
Normal Displacement ◽  
Linear Temperature ◽  
Content Type ◽  
Wide Range ◽  
Eigen Value ◽  
Thermally Conducting

PurposeThe two-dimensional deformation of a homogeneous, thermally conducting, monoclinic material has been studied by using Laplace and Fourier transforms technique. A linear temperature ramping function is used to more realistically model: thermal loading of the half-space surface. The general solution obtained is applied to a specific problem of a half-space subjected to ramp-type heating and loading. The displacements, stresses and temperature distribution so obtained in the physical domain are computed numerically and illustrated graphically. The comparison for Lord-Shulman (L-S), Green and Lindsay (G–L), Green and Naghdi (G–N) and Chandrasekharaiah and Tzou (CTU) theories have been shown graphically to estimate the effect of ramping parameter of heating for an insulated and temperature gradient boundaries.Design/methodology/approachThe design of the study is eigenvalue approachFindingsHomogeneous, thermally conducting monoclinic material has been taken under consideration to study the effect of linear temperature ramping parameter on temperature and normal displacement field. It is observed that magnitude of field quantities is large near the point of application of source for the non-dimensional values of time in all the four models. The numerical values for the field quantities are computed graphically for a wide range of values of finite pulse rise-time in the two situations t0 < t, t0 > t for generalized thermoelasticity theories.Originality/value(1) Governing equations for homogeneous, t0 thermally conducting, monoclinic material are described and solved. (2) Eigen value approach is used to solve the problem. (3) The effect of ramping parameter of heating has been studied for various models of the thermoelasticity to show the comparision between them.

Dispersive Pulse Propagation Parallel to the Interfaces of a Laminated Composite

1969 ◽  
Vol 36 (3) ◽  
pp. 479-484 ◽  
Author(s):  
J. C. Peck ◽  
G. A. Gurtman
Keyword(s):  
Wave Propagation ◽  
Half Space ◽  
Fourier Transforms ◽  
Formal Solution ◽  
Low Frequency ◽  
Laminated Composite ◽  
Propagation Distance ◽  
Step Function ◽  
Algebraic Expression ◽  
Mathematical Treatment

This paper presents a theoretical analysis of the geometric dispersion of transient stress waves in a linearly elastic laminated composite. The loading is a uniform pressure of step-function time-dependence, applied to a half space. The laminates are perpendicular to the half-space boundary. The mathematical treatment is borrowed from the theory of wave propagation in rods. Fourier transforms are applied to time and the coordinate in the propagation direction. Inversion of the spatial transform by residues yields a formal solution in the form of an infinite series of integrals. Each of these integrals is the contribution to the transient response from a mode of sinusoidal wave propagation. Application of the saddle-point technique for long-time asymptotic approximation indicates that the low-frequency portion of the integral from the first mode gives the dominant contribution, called the head-of-the-pulse approximation. The form of the expression for the head-of-the-pulse approximation leads to the definition of a characteristic dispersion time τ. Since τ is a single quantity which describes the dispersion of the wave, it simplifies parametric studies. A closed-form algebraic expression for τ is presented, which has a simple dependence on the propagation distance and spacing of the laminates. Numerical examples for boron-epoxy and glass-epoxy laminates are given.

Identification of Vertical Exciting Force on the Surface of an Elastic Half-Space Using Sensor Fusion

2006 ◽  
Author(s):  
Hamid R. Hamidzadeh ◽  
Albert C. J. Luo
Keyword(s):  
Half Space ◽  
Fourier Transforms ◽  
Elastic Half Space ◽  
Exciting Force ◽  
Dynamic Responses ◽  
Numerical Techniques ◽  
Concentrated Force ◽  
Analytical Technique ◽  
Homogeneous Half Space ◽  
Sensors Fusion

An analytical technique for identification of the location of an unknown vertical exciting force on the surface of ground using sensors fusion is presented. The analysis is based on the dynamic responses of points on the surface of an elastic half-space medium subjected to a vertical, harmonic and concentrated force on the surface. The medium is assumed to be an elastic, isotropic and homogeneous half-space. The problem is analytically formulated by employing double Fourier transforms, and the solution is obtained in the form of integral expressions in terms of Rayleigh functions. Numerical techniques are utilized for the computation of integrals presented by the inverse transforms. Non-dimensional values for the in-phase and quadrature components of the displacements for any position on the surface of the unloaded half-space in terms of frequency and position of the exciting force are presented for a Poisson's ratio of 0.25.

Measures with Fourier Transforms in L2 of a Half-space

2011 ◽  
Vol 54 (1) ◽  
pp. 172-179
Author(s):  
Bassam Shayya
Keyword(s):  
Fourier Transform ◽  
Lebesgue Measure ◽  
Half Space ◽  
Fourier Transforms ◽  
Geometric Information ◽  
Absolutely Continuous ◽  
Compactly Supported ◽  
The Fourier Transform

AbstractWe prove that if the Fourier transform of a compactly supported measure is in L2 of a half-space, then the measure is absolutely continuous to Lebesgue measure. We then show how this result can be used to translate information about the dimensionality of a measure and the decay of its Fourier transform into geometric information about its support.

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