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Half-space

About: Half-space is a research topic. Over the lifetime, 2264 publications have been published within this topic receiving 33563 citations.


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TL;DR: In this paper, it was shown that a proper surface wave may always occur in a stable linear anisotropic half space provided that a certain real symmetric 3*3 matrix B is not positive definite for all velocities less than a limiting velocity nu L, the velocity at which bulk wave solutions first appear.
Abstract: From a previous analysis it is known that a proper surface wave may always occur in a stable linear anisotropic half space provided that a certain real symmetric 3*3 matrix B is not positive definite for all velocities less than a limiting velocity nu L, the velocity at which bulk wave solutions first appear. B is also the lagrangian factor matrix for a particular straight dislocation moving uniformly in an infinite medium which is elastically identical to the half space. By examining the behaviour of the dislocation lagrangian and the eigenvalues of B at nu L, it is proved that proper surface waves may always occur except in cetain special cases. In each special case there always exists at least one bulk wave solution which satisfies the free surface condition on the half space boundary. Thus, there exist no forbidden directions for steady state propagation satisfying the free surface condition, i.e. either a proper (attenuated) surface wave and/or an unattenuated 'bulk surface wave' solution is possible. One simple numerical integration suffices to determine if a given propagation direction admits a proper surface solution.

154 citations

Journal ArticleDOI
TL;DR: In this paper, the basic governing equations for isotropic and homogeneous generalized thermoelastic half-space under hydrostatic initial stress are formulated in the context of the Green and Naghdi theory of types II and III.

147 citations

Journal ArticleDOI
TL;DR: In this article, the displacement field is analyzed using multi-integral transforms and an inversion scheme based on the well-known Cagniard technique, which reduces the displacements to single integral and algebraic contributions, each of which is identified as the disturbance behind a specific wave front.
Abstract: The propagation of transient waves in an elastic half-space excited by a traveling normal point load is investigated. The load is suddenly applied and then it moves rectilinearly at a constant speed along the free surface. The displacements are computed for all points of the half-space as well as for all load speeds. The disturbance is analyzed by using multi-integral transforms and an inversion scheme based on the well-known Cagniard technique. This reduces the displacements to single integral and algebraic contributions, each of which is identified as the disturbance behind a specific wave front. The same solution is valid for all load speeds, even though the wave front geometry varies greatly, depending on the speed of the load relative to the body wave speeds. Moreover, the surface displacements are obtained from the interior ones, but only after the Rayleigh waves are computed by a separate calculation. Then, by taking advantage of the form of the exact solution, wave front expansions and Rayleigh wave approximations are computed for all load speeds. Several other analytical results are obtained for restricted values of the load speed. In particular, when it exceeds both of the body wave speeds the steady-state displacement field is separated from the transient one and reduced to algebraic form. Also, for the limit case of zero load speed a new representation of the interior displacements for Lamb's point load problem is displayed in terms of single integrals.

147 citations

Journal ArticleDOI
TL;DR: This paper shows how two sets can be strictly separated by one or more planes or surfaces (nonlinear manifolds) via linear programming.
Abstract: Let two sets of patterns be represented by two finite point sets in an n -dimensional Euclidean space E^{n} . If the convex hulls of the two sets do not intersect, the sets can be strictly separated by a plane. Such a plane can be constructed by the Motzkin-Schoenberg error-correction procedure or by linear programming. More often than not, however, the convex hulls of the two point sets do intersect, in which case strict separation by a plane is not possible any more. One may then resort to separation by more than one plane. In this paper, we show how two sets can be strictly separated by one or more planes or surfaces (nonlinear manifolds) via linear programming. A computer program that implements the present method has been written and successfully tested on a number of real problems.

146 citations

Journal ArticleDOI
TL;DR: In this article, the displacement stress field produced at any point of a linear homogeneous and isotropic viscoelastic half space by an arbitrary time dependent distribution of pressure acting on its boundary is analyzed.

144 citations


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Performance
Metrics
No. of papers in the topic in previous years
YearPapers
202343
202274
202160
202049
201979
201848