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.

Contact Stress Analysis of a Layered Transversely Isotropic Half-Space

1992 ◽  
Vol 114 (2) ◽  
pp. 253-261 ◽  
Author(s):  
C. H. Kuo ◽  
L. M. Keer
Keyword(s):  
Half Space ◽  
Mixed Boundary ◽  
Contact Region ◽  
Three Dimensional ◽  
Transversely Isotropic ◽  
Hankel Transform ◽  
Elastic Half Space ◽  
Contact Stresses ◽  
Stress Components ◽  
Contact Failure

The three-dimensional problem of contact between a spherical indenter and a multi-layered structure bonded to an elastic half-space is investigated. The layers and half-space are assumed to be composed of transversely isotropic materials. By the use of Hankel transforms, the mixed boundary value problem is reduced to an integral equation, which is solved numerically to determine the contact stresses and contact region. The interior displacement and stress fields in both the layer and half-space can be calculated from the inverse Hankel transform used with the solved contact stresses prescribed over the contact region. The stress components, which may be related to the contact failure of coatings, are discussed for various coating thicknesses.

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 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.

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 Mathematical Modeling of Vibration Dampers of Vibration-Insulated Structures

2021 ◽  
Vol 248 ◽  
pp. 02009
Author(s):  
Evgeny Sosenushkin ◽  
Oksana Ivanova ◽  
Elena Yanovskaya ◽  
Yuliya Vinogradova
Keyword(s):  
Half Space ◽  
Vibration Isolation ◽  
Dynamic Effect ◽  
Contact Problems ◽  
Dynamic Contact ◽  
Manufacturing Cost ◽  
Harmonic Load ◽  
Model Soil ◽  
Homogeneous Half Space ◽  
Vibration Dampers

Vibration dampers are installed on the machine foundations in order to reduce the vibration level. Such technological solutions are most expedient in the case of a harmonic load with a low instability of the vibration frequency. Unfortunately, dampers do not provide such a large reduction in the dynamic effect on the base, as vibration isolation, but in some cases their efficiency turns out to be quite sufficient with a relatively simple implementation and low manufacturing cost. The use of dynamic vibration dampers gives a great effect when an increased vibration of foundations occurs during the operation of equipment in metallurgical production, for example, when processing materials by pressure, reconstructing enterprises and replacing heavy equipment. During the operation of heavy forging equipment and manipulators for various purposes, the foundations of these devices can be considered as a rigid body. The model soil on which this foundation is installed can be considered a homogeneous elastic isotropic half-space. When calculating with such mathematical models, one can use solutions of the corresponding dynamic contact problems. A comparative analysis of the effectiveness of damping foundation vibrations using different foundation models, including the model of an elastic, homogeneous half-space and a system of semi-infinite rods, the modulus of elasticity of which increases with depth according to the quadratic law, shows a fairly close agreement.

scholarly journals Surface waves guided by topography in an anisotropic elastic half-space

2013 ◽  
Vol 469 (2149) ◽  
pp. 20120371 ◽  
Author(s):  
Y. B. Fu ◽  
G. A. Rogerson ◽  
W. F. Wang
Keyword(s):  
Surface Wave ◽  
Surface Waves ◽  
Half Space ◽  
Wave Speed ◽  
Elastic Half Space ◽  
Simple Eigenvalue ◽  
Plane Shear ◽  
Number Of Factors ◽  
Present Context ◽  
Anisotropic Elastic

We consider the propagation of free surface waves on an elastic half-space that has a localized geometric inhomogeneity perpendicular to the direction of wave propagation (such waves are known as topography-guided surface waves). Our aim is to investigate how such a weak inhomogeneity modifies the surface-wave speed slightly. We first recover previously known results for isotropic materials and then present additional results for a generally anisotropic elastic half-space assuming only one plane of material symmetry. It is shown that a topography-guided surface wave in the present context may or may not propagate depending on a number of factors. In particular, they cannot propagate if the original two-dimensional surface wave on a flat half-space is supersonic with respect to the speed of anti-plane shear waves. For the case when a topography-guided surface wave may exist, the existence and computation of wave speed correction is reduced to the solution of a simple eigenvalue problem whose properties are previously well understood. As a by-product of our analysis, we deduce that there exists at least one topography-guided surface wave on an isotropic elastic half-space, and that it is unique when the geometric inhomogeneity has sufficiently small amplitude.

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.

Sign in / Sign up

Export Citation Format

Share Document