Viscous-Elastic Half-Space Vibration Stimulated by High-Speed Moving Loads of Different Speeds

2012 ◽  
Vol 518-523 ◽  
pp. 3874-3877
Author(s):  
Tao Qian ◽  
Xiao Ping Shui ◽  
Yong Fa Zhang ◽  
Yong Gang Guo ◽  
Meng Ma
Keyword(s):  
Half Space ◽  
Coordinate Transformation ◽  
High Speed ◽  
Three Dimensional ◽  
Elastic Half Space ◽  
Moving Loads ◽  
Cylindrical Coordinates ◽  
Relative Coordinate ◽  
The Laplace Transform ◽  
Practical Security

A rule of response of an infinite viscous-elastic half-space stimulated by the moving loads of different speeds is outlined in this paper. In order to obtain a three-dimensional analytical solution of the Viscous-elastic half-space with the moving loads of different speeds, the Laplace transform and relative coordinate transformation in cylindrical coordinates are used. Then, the IFFT and relative coordinate transformation are used to solve two-dimensional infinite integration which can greatly improve the operational efficiency. The rules of responses of different velocities from the results by using the principle of dynamics and energy dissipation are also analyzed and induced in this paper, and obtain the incentives of displacement distortion by the super-Rayleigh wave velocity at surface. The results could be referred in improving the practical security in the project.

Guided Surface Waves on an Elastic Half Space

1971 ◽  
Vol 38 (4) ◽  
pp. 899-905 ◽  
Author(s):  
L. B. Freund
Keyword(s):  
Wave Propagation ◽  
Surface Wave ◽  
Surface Waves ◽  
Half Space ◽  
Body Wave ◽  
Three Dimensional ◽  
Elastic Half Space ◽  
Normal Displacement ◽  
Rigid Barrier ◽  
Wave Disturbances

Three-dimensional wave propagation in an elastic half space is considered. The half space is traction free on half its boundary, while the remaining part of the boundary is free of shear traction and is constrained against normal displacement by a smooth, rigid barrier. A time-harmonic surface wave, traveling on the traction free part of the surface, is obliquely incident on the edge of the barrier. The amplitude and the phase of the resulting reflected surface wave are determined by means of Laplace transform methods and the Wiener-Hopf technique. Wave propagation in an elastic half space in contact with two rigid, smooth barriers is then considered. The barriers are arranged so that a strip on the surface of uniform width is traction free, which forms a wave guide for surface waves. Results of the surface wave reflection problem are then used to geometrically construct dispersion relations for the propagation of unattenuated guided surface waves in the guiding structure. The rate of decay of body wave disturbances, localized near the edges of the guide, is discussed.

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.

Deformation of a layered, elastic, half-space by uniformly moving line loads

1970 ◽  
Vol 60 (1) ◽  
pp. 167-191 ◽  
Author(s):  
J. W. Dunkin ◽  
D. G. Corbin
Keyword(s):  
Half Space ◽  
High Speed ◽  
Static Solution ◽  
Elastic Half Space ◽  
Dispersion Relations ◽  
Line Integral ◽  
Trapped Mode ◽  
Mode Dispersion ◽  
Moving Line ◽  
Line Loads

abstract When a layered half-space is subjected to loads which move uniformly along its surface, the deformation of the half-space depends on the manner in which the load couples into the surface-wave modes. The uniform speed of the load selects those parts of the modal spectra that have phase velocities equal to the load speed. The restriction that the phase velocity be real leads to novel dispersion relations for the leaky modes, but the trapped mode dispersion relations are the usual ones. In this paper general expressions are derived for the solution for uniformly moving line loads on an elastic half-space containing an arbitrary number of layers. In addition to the modal contributions, the solution contains contributions from source singularities and a line integral that reduce to the static solution as the load speed tends to zero. The details are worked out for the special case of a single low-speed layer lying on a high-speed half-space. For the modes, real and imaginary parts of frequency and velocity amplitudes at various depths are presented as functions of frequency. Total velocity waveforms are shown for selected load speeds and depths.

Transient Thermoelastic Stress Fields in a Half-Space

2002 ◽  
Vol 125 (1) ◽  
pp. 33-43 ◽  
Author(s):  
Shuangbiao Liu ◽  
Qian Wang
Keyword(s):  
Stress Field ◽  
Half Space ◽  
Frictional Heating ◽  
Three Dimensional ◽  
Thermoelastic Stress ◽  
Parabolic Type ◽  
Elastic Half Space ◽  
Transform Method ◽  
Rough Surface Contact ◽  
Thermoelastic Stress Field

Computing the thermoelastic stress field of a material subjected to frictional heating is essential for component failure prevention and life prediction. However, the analysis for three-dimensional thermoelastic stress field for tribological problems is not well developed. Furthermore, the pressure distribution due to rough surface contact is irregular; hence the frictional heating can hardly be described by an analytical expression. This paper presents a novel set of frequency-domain expressions (frequency response functions) of the thermoelastic stress field of a uniformly moving three-dimensional elastic half-space subjected to arbitrary transient frictional heating, where the velocity of the half-space, its magnitude and direction, can be an arbitrary function of time. General formulas are expressed in the form of time integrals, and important expressions for constant velocities are given for the transient-instantaneous, transient-continuous, and steady-state cases. The thermoelastic stress field inside a translating half-space with constant velocities are illustrated and discussed by using the discrete convolution and fast Fourier transform method when a parabolic type or an irregularly distributed heat source is applied.

The Transition Matrix Formalism for the Scattering of an Alluvium on an Elastic Half-Space

2007 ◽  
Author(s):  
Wen-I Liao ◽  
Tsung-Jen Teng ◽  
Shiang-Jung Wang
Keyword(s):  
Half Space ◽  
Transition Matrix ◽  
Plane Waves ◽  
Three Dimensional ◽  
Scattering Matrix ◽  
Elastic Half Space ◽  
Basis Functions ◽  
Matrix Formalism ◽  
T Matrix ◽  
Singular Wave

This paper develops the transition matrix formalism for scattering from an three-dimensional alluvium on an elastic half-space. Betti’s third identity is employed to establish orthogonality conditions among basis functions that are Lamb’s singular wave functions. The total displacements and associated tractions exterior and interior to the surface are expanded in a Rayleigh series. The boundary conditions are applied and the T-matrix is derived. A linear transformation is utilized to construct a set of orthogonal basis functions. The transformed T-matrix is related to the scattering matrix and it is shown that the scattering matrix is symmetric and unitary and that the T-matrix is symmetric. Typical numerical results obtained by incident plane waves for verification are presented.

THREE-DIMENSIONAL SURFACE CRACK ANALYSIS OF ELASTIC HALF-SPACE UNDER ROLLING CONTACT LOAD

2009 ◽  
Vol 06 (02) ◽  
pp. 317-332 ◽  
Author(s):  
MENG-CHENG CHEN ◽  
HUI-QIN YU
Keyword(s):  
Numerical Solution ◽  
Integral Equations ◽  
Half Space ◽  
Three Dimensional ◽  
Elastic Half Space ◽  
Rolling Contact ◽  
Contact Load ◽  
Hypersingular Integral ◽  
Space Body ◽  
Planar Crack

In this work a three-dimensional planar crack on the surface of elastic half-space was analyzed under rolling contact load. The stresses interior to an elastic half-space body under rolling contact load and those produced by an infinitesimal displacement jump loop for the elastic half-space body were used to reduce the planar crack problem to the solution of a system of two-dimensional hypersingular integral equations with unknown displacement jump. The ideas of finite element discretization were employed to construct numerical solution schemes for solving the integral equations. An appropriate treatment of the associated hypersingular integral in the numerical solution to the integral equations was proposed in Hadamard's finite-part integral sense. The numerical results showed that the present procedure yields solutions with high accuracies. The stress intensity factors near the crack front edge under rolling contact load were indicated in graphical form with varying the crack shape, the radius of rolling contact zone and the friction coefficients, respectively. In addition, the influence of the lubricant infiltrating the crack surfaces on the crack propagation was also discussed in the paper.

Bond of tube in semi-infinite elastic solid

1980 ◽  
Vol 15 (2) ◽  
pp. 53-62 ◽  
Author(s):  
J W Ivering
Keyword(s):  
Half Space ◽  
Three Dimensional ◽  
Elastic Solid ◽  
Elastic Half Space ◽  
Infinite Medium ◽  
Bond Stress ◽  
Elastic Analysis ◽  
One Dimensional ◽  
Stress Curve ◽  
Tube Segment

The analysis of the bond stress of a thick-walled tube embedded at the surface of an elastic, isotropic, semi-infinite medium is presented. The condition of three-dimensional compatibility between the tube and the anchorage medium is taken into account. An equilibrium equation for a segment of an embedded tube is derived, from which bond stresses acting on the tube can be computed. The general solution obtained relates to the vector function for a uniform lineal load acting perpendicularly to the surface of an elastic half-space. The solution is in agreement with equations derived independently for cases of one-dimensional (lineal) compatibility. The equation of equilibrium derived for a tube segment embedded at the surface of an elastic half-space is transformed to a form suitable for solving the bond stresses of a tube anchorage embedded at some distance from the surface. A numerical solution of bond stresses obtained by elastic analysis is compared to the bond stress curve along the anchorage obtained experimentally.

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.

Modeling of ultra-high-speed impact at the surface of an elastic half-space

Wave Motion ◽  
2015 ◽  
Vol 58 ◽  
pp. 77-100 ◽  
Author(s):  
Mandikizinoyou Taro ◽  
Thibaut Chaise ◽  
Daniel Nelias
Keyword(s):  
Half Space ◽  
High Speed ◽  
Elastic Half Space ◽  
High Speed Impact ◽  
Ultra High Speed

Transient fundamental solutions for a transversely isotropic elastic half space

1993 ◽  
Vol 442 (1916) ◽  
pp. 505-531 ◽  
Keyword(s):  
Half Space ◽  
Transient Response ◽  
Analytical Solutions ◽  
Three Dimensional ◽  
Transversely Isotropic ◽  
Integral Transforms ◽  
Fundamental Solutions ◽  
Elastic Half Space ◽  
Kernel Functions ◽  
Two Dimensional

This paper is concerned with the study of transient response of a transversely isotropic elastic half-space under internal loadings and displacement discontinuities. Governing equations corresponding to two-dimensional and three-dimensional transient wave propagation problems are solved by using Laplace–Fourier integral transforms and Laplace−Hankel integral transforms, respectively. Explicit general solutions for displacements and stresses are presented. Thereafter boundary-value problems corresponding to internal transient loadings and transient displacement discontinuities are solved for both two-dimensional and three-dimensional problems. Explicit analytical solutions for displacements and stresses corresponding to internal loadings and displacement discontinuities are presented. Solutions corresponding to arbitrary loadings and displacement discontinuities can be obtained through the application of standard analytical procedures such as integration and Fourier expansion to the fundamental solutions presented in this article. It is shown that the transient response of a medium can be accurately computed by using a combination of numerical quadrature and a numerical Laplace inversion technique for the evaluation of integrals appearing in the analytical solutions. Comparisons with existing transient solutions for isotropic materials are presented to confirm the accuracy of the present solutions. Selected numerical results for displacements and stresses due to a buried circular patch load are presented to portray some features of the response of a transversely isotropic elastic half-space. The fundamental solutions presented in this paper can be used in the analysis of a variety of transient problems encountered in disciplines such as seismology, earthquake engineering, etc. In addition these fundamental solutions appear as the kernel functions in the boundary integral equation method and in the displacement discontinuity method.

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