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.

scholarly journals Rayleigh-type waves on a coated elastic half-space with a clamped surface

2019 ◽  
Vol 377 (2156) ◽  
pp. 20190111 ◽  
Author(s):  
J. Kaplunov ◽  
D. Prikazchikov ◽  
L. Sultanova
Keyword(s):  
Half Space ◽  
Numerical Solutions ◽  
Substrate Surface ◽  
Numerical Data ◽  
Elastic Half Space ◽  
Asymptotic Results ◽  
Homogeneous Half Space ◽  
Upper Face ◽  
Localized Waves ◽  
Perturbed Equation

Elastodynamics of a half-space coated by a thin soft layer with a clamped upper face is considered. The focus is on the analysis of localized waves that do not exist on a clamped homogeneous half-space. Non-traditional effective boundary conditions along the substrate surface incorporating the effect of the coating are derived using a long-wave high-frequency procedure. The derived conditions are implemented within the framework of the earlier developed specialized formulation for surface waves, resulting in a perturbation of the shortened equation of surface motion in the form of an integral or pseudo-differential operator. Non-uniform asymptotic formula for the speeds of the sought for Rayleigh-type waves, failing near zero frequency and the thickness resonances of a layer with both clamped faces, follow from the aforementioned perturbed equation. Asymptotic results are compared with the numerical solutions of the full dispersion relation for a clamped coated half-space. A similarity with Love-type waves proves to be useful for interpreting numerical data. This article is part of the theme issue ‘Modelling of dynamic phenomena and localization in structured media (part 1)’.

scholarly journals The use of modelling of impacts exerted by means of transport on the environment for ensuring safety

2018 ◽  
Vol 188 (2) ◽  
pp. 162-175
Author(s):  
Joanna Bril ◽  
Edward Rydygier
Keyword(s):  
Rigid Body ◽  
Half Space ◽  
Dynamic Properties ◽  
Elastic Half Space ◽  
Transport Systems ◽  
Concentrated Force ◽  
Foundation Soil ◽  
Infinite Mass ◽  
Model Research ◽  
Surface Rayleigh Wave

The article presents the model research on impacts exerted by means of transport on the structures. In modelling the dynamics of transport systems the dynamic properties of the ground forming the foundation soil for tracks or roadways have been taken into account. The ground has been modelled as an elastic half-space. The dynamics of an infinite mass band being in contact with an elastic half-space has been investigated. As part of the research on impacts exerted by means of transport on structures a model of a problem has been examined where an automotive vehicle, representing a concentrated force in motion, is in contact with a roadway described as a rigid body coupled with an elastic half-space. It has been demonstrated that a surface (Rayleigh) wave propagates in the ground, being a continuous (elastic) medium, and acts on a structure modelled as a rigid body. The research results have been presented in the form of vertical and horizontal transmittances of the ground for different frequencies of loading with different unit forces.

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.

scholarly journals Refined boundary conditions on the free surface of an elastic half-space taking into account non-local effects

2016 ◽  
Vol 472 (2186) ◽  
pp. 20150800 ◽  
Author(s):  
R. Chebakov ◽  
J. Kaplunov ◽  
G. A. Rogerson
Keyword(s):  
Boundary Layer ◽  
Free Surface ◽  
Boundary Conditions ◽  
Half Space ◽  
Elastic Half Space ◽  
Interior Solution ◽  
Homogeneous Half Space ◽  
Classical Boundary ◽  
Non Local ◽  
Rayleigh Wave Speed

The dynamic response of a homogeneous half-space, with a traction-free surface, is considered within the framework of non-local elasticity. The focus is on the dominant effect of the boundary layer on overall behaviour. A typical wavelength is assumed to considerably exceed the associated internal lengthscale. The leading-order long-wave approximation is shown to coincide formally with the ‘local’ problem for a half-space with a vertical inhomogeneity localized near the surface. Subsequent asymptotic analysis of the inhomogeneity results in an explicit correction to the classical boundary conditions on the surface. The order of the correction is greater than the order of the better-known correction to the governing differential equations. The refined boundary conditions enable us to evaluate the interior solution outside a narrow boundary layer localized near the surface. As an illustration, the effect of non-local elastic phenomena on the Rayleigh wave speed is investigated.

scholarly journals Contact Analyses for Anisotropic Half Space With an Anisotropic Coating

2012 ◽  
Author(s):  
C. Bagault ◽  
D. Nélias ◽  
M.-C. Baietto ◽  
T. Ovaert
Keyword(s):  
Half Space ◽  
Elastic Half Space ◽  
Rigid Sphere ◽  
Manufacturing Processes ◽  
Problem Solution ◽  
Numerical Techniques ◽  
General Anisotropy ◽  
Recent Developments ◽  
Anisotropic Elastic ◽  
Wear Coatings

For most composite and mono-crystal materials their compositions or the elaboration and manufacturing processes imply that it exists one or two main directions or even a general anisotropy. Moreover, coatings are often used to prevent or control wear. Coatings do not have, generally, the same properties as the substrate and may have various thicknesses. The influence of the anisotropy orientations (in the coating and in the substrate) have to be taken into account to better predict the distribution of the contact pressure and the subsurface stress-field in order to optimize the service life of industrial components. A contact model using semi analytical methods, relying on elementary analytical solutions, has been developed. It is based on numerical techniques adapted to contact mechanics. Recent developments aim to quantify displacements and stresses of a layered anisotropic elastic half space which is in contact with a rigid sphere. The influence of material properties and layer thickness on the contact problem solution will be more specifically analyzed.

Elastic Displacement and Stress Fields Induced by a Dislocation of Polygonal Shape in an Anisotropic Elastic Half-Space

2012 ◽  
Vol 79 (2) ◽  
Author(s):  
H. J. Chu ◽  
E. Pan ◽  
J. Wang ◽  
I. J. Beyerlein
Keyword(s):  
Half Space ◽  
Dislocation Loop ◽  
Hydrostatic Stress ◽  
Jump Condition ◽  
Elastic Half Space ◽  
Biaxial Stress ◽  
Stress Fields ◽  
Elastic Displacement ◽  
Homogeneous Half Space ◽  
Anisotropic Elastic

The elastic displacement and stress fields due to a polygonal dislocation within an anisotropic homogeneous half-space are studied in this paper. Simple line integrals from 0 to π for the elastic fields are derived by applying the point-force Green’s functions in the corresponding half-space. Notably, the geometry of the polygonal dislocation is included entirely in the integrand easing integration for any arbitrarily shaped dislocation. We apply the proposed method to a hexagonal shaped dislocation loop with Burgers vector along [1¯ 1 0] lying on the crystallographic (1 1 1) slip plane within a half-space of a copper crystal. It is demonstrated numerically that the displacement jump condition on the dislocation loop surface and the traction-free condition on the surface of the half-space are both satisfied. On the free surface of the half-space, it is shown that the distributions of the hydrostatic stress (σ11 + σ22)/2 and pseudohydrostatic displacement (u1 + u2)/2 are both anti-symmetric, while the biaxial stress (σ11 − σ22)/2 and pseudobiaxial displacement (u1 − u2)/2 are both symmetric.

scholarly journals Two-Parametric Analysis of Anti-Plane Shear Deformation of a Coated Elastic Half-Space

2018 ◽  
Vol 12 (4) ◽  
pp. 270-275
Author(s):  
Leyla Sultanova
Keyword(s):  
Shear Deformation ◽  
Half Space ◽  
Elastic Half Space ◽  
Harmonic Load ◽  
Plane Shear ◽  
Low Contrast ◽  
Homogeneous Half Space ◽  
Deformation Problem ◽  
Stress Components ◽  
Effective Boundary Condition

Abstract The anti-plane shear deformation problem of a half-space coated by a soft or a stiff thin layer is considered. The two-term asymptotic analysis is developed motivated by the scaling for the displacement and stress components obtained from the exact solution of a model problem for a shear harmonic load. It is shown that for a rather high contrast in stiffness of the layer and the half-space Winkler-type behaviour appears for a relatively soft coating, while for a relatively stiff one, the equations of plate shear are valid. For low contrast, an alternative approximation is suggested based on the reduced continuity conditions and the fact that the applied load may be transmitted to the interface. In case of a stiff layer, a simpler problem for a homogeneous half-space with effective boundary condition is also formulated, modelling the effect of the coating, while for a relatively soft layer a uniformly valid approximate formula is introduced.

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