# Pulse generation in an elastic half space by normal pressure

TL;DR: In this article, the Cagniard De-Hoop technique was used to generate a pulse in an elastic half space by impulsive normal pressure over a circular area on the surface.

About: This article is published in International Journal of Engineering Science.The article was published on 1975-07-01. It has received 9 citations till now. The article focuses on the topics: Pulse (physics) & Displacement field.

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TL;DR: In this paper, an earthquake source is simulated as a simple finite source, and the transient response of the surface displacement of an elastic half space due to the above internal source is calculated, using a series of transformations, followed by the traditional Cagniard-de Hoop technique.

Abstract: An earthquake source has been simulated as a simple finite source, i.e., normal pressure acting over an inclined fault plane. The transient response of the surface displacement of an elastic half space due to the above internal source is calculated. A series of transformations, followed by the traditional Cagniard–de Hoop technique, are used to compute the transient response. Various wave arrivals are discussed. Numerical computations bring out the special character of the finite source vis-a-vis the point source. The originality of the paper lies in the fact that for the first time an exact computation of the surface response due to an inclined finite source has been computed by Cagniard’s approach.

11 citations

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TL;DR: In this article, the response of an elastic half space to a realistic model of faulting is considered, where a dislocation is developed along a line of finite length and then moves nonuniformly along an inclined plane (fault) surface.

8 citations

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TL;DR: In this paper, exact expressions for the displacement field in a homogeneous isotropic elastic half space whose surface is subjected to a unit normal pressure are obtained in the form of triple integrals over finite ranges.

6 citations

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06 Dec 2019TL;DR: Linear and Non-Linear Deformations of Elastic Solids as discussed by the authors aims to compile the advances in the field of linear and non-linear elasticity through discussion of advanced topics.

Abstract: Linear and Non-Linear Deformations of Elastic Solids aims to compile the advances in the field of linear and non-linear elasticity through discussion of advanced topics. Broadly classified into two parts, it includes crack, contact, scattering and wave propagation in linear elastic solids and bending vibration, stability in non-linear elastic solids supported by MATLAB examples. This book is aimed at graduate students and researchers in applied mathematics, solid mechanics, applied mechanics, structural mechanics and includes comprehensive discussion of related analytical/numerical methods.

5 citations

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TL;DR: In this paper, a displacement field is obtained by the use of Cagniard-De-Hoop technique and different wave fronts expected are identified and nature of approximate form of displacement near wave fronts are discussed.

2 citations

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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

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TL;DR: In this article, the solution to compressible flow problems under fully assigned boundary conditions is discussed, and it is shown that Schwarz's results on minimal surfaces can be immediately applied for two-dimensional flow, and several special cases and examples are given.

Abstract: The solution to compressible flow problems under fully assigned boundary conditions is discussed. It is shown that Schwarz's results on minimal surfaces can be immediately applied for two-dimensional flow, and several special cases and examples are given. Extensions of these results provide certain particular types of three-dimensional flow.

71 citations

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TL;DR: In this article, the first terms of asymptotic series in powers of t−t0 are obtained by evaluating the integral form of the Laplace transform of the time solution by the saddle point method or a variation of it.

Abstract: Techniques are presented for approximating integral solutions to some problems in theoretical seismology. The approximations obtained are the first terms of asymptotic series in powers of t−t0, where t is the time and t0 is an arrival time. The approximations are obtained by evaluating the integral form of the Laplace transform of the time solution by the saddle point method or a variation of it. To the resulting expression is applied a Tauberian limit theorem from which is obtained the time solution. Two examples are given which illustrate some of the specific techniques for the use of the method.

36 citations

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TL;DR: An exact solution to a class of three-dimensional half-space pulse propagation problems in elasticity is developed in a simple way through the use of the extended Bateman-Pekeris theorem as discussed by the authors.

26 citations

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TL;DR: In this article, the Laplace transforms of the displacement components of an axisymmetrical poloidal pulse were derived for a semi-infinite, homogeneous, isotropic elastic solid by applying a uniform time-dependent normal pressure over a circular portion of the surface of the half-space.

7 citations