# Pulse generation in an elastic half-space by the uniform normal loading of a circular surface segment

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.

About: This article is published in International Journal of Engineering Science.The article was published on 1970-07-01. It has received 7 citations till now. The article focuses on the topics: Displacement field & Circular surface.

##### Citations

More filters

••

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

••

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.

9 citations

••

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

••

TL;DR: In this paper, the residual variable method (RVM) is used to obtain exact closed-form solutions of the wave propagation problems in an infinite, elastic medium with and without a shell embedment.

Abstract: A spherical cavity in an infinite, elastic medium with and without a shell embedment is subjected to axisymmetric, non-torsional surface loads in the radial and meridional directions. The so-called Residual Variable Method (RVM) is used to obtain exact, closed-form solutions of the wave propagation problems. Some representative numerical results are presented graphically for the stresses created in two realistic loading situations.

5 citations

### Cites methods from "Pulse generation in an elastic half..."

...Particular attention was given to the evolving complicated pattern of wavefronts generated when the load is only over a cap with the remainder of the surface stress-free using techniques similar to those utilized by Tupholme [17] in the analogous half-space problem....

[...]

••

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

##### References

More filters

•

01 Jan 1944

TL;DR: The tabulation of Bessel functions can be found in this paper, where the authors present a comprehensive survey of the Bessel coefficients before and after 1826, as well as their extensions.

Abstract: 1. Bessel functions before 1826 2. The Bessel coefficients 3. Bessel functions 4. Differential equations 5. Miscellaneous properties of Bessel functions 6. Integral representations of Bessel functions 7. Asymptotic expansions of Bessel functions 8. Bessel functions of large order 9. Polynomials associated with Bessel functions 10. Functions associated with Bessel functions 11. Addition theorems 12. Definite integrals 13. Infinitive integrals 14. Multiple integrals 15. The zeros of Bessel functions 16. Neumann series and Lommel's functions of two variables 17. Kapteyn series 18. Series of Fourier-Bessel and Dini 19. Schlomlich series 20. The tabulation of Bessel functions Tables of Bessel functions Bibliography Indices.

9,584 citations

••

TL;DR: In this paper, Elastic Waves in Layered Media (ELMW) are used to describe the properties of layered media in a geologiska foreningen i Stockholm Forhandlingar.

Abstract: (1958). Elastic Waves in Layered Media. Geologiska Foreningen i Stockholm Forhandlingar: Vol. 80, No. 1, pp. 128-129.

1,687 citations

••

01 Jan 1904-Philosophical transactions - Royal Society. Mathematical, physical and engineering sciences

TL;DR: In this paper, the propagation of vibrations over the surface of a "semi-infinite" isotropic elastic solid, i.e., a solid bounded only by a plane, is considered.

Abstract: 1. This paper treats of the propagation of vibrations over the surface of a “semiinfinite” isotropic elastic solid, i. e. ,a solid bounded only by a plane. For purposes of description this plane may be conceived as horizontal, and the solid as lying below it, although gravity is not specially taken into account. The vibrations are supposed due to an arbitrary application of force at a point. In the problem most fully discussed this force consists of an impulse applied vertically to the surface; but some other cases, including that of an internal source of disturbance, are also (more briefly) considered. Owing to the complexity of the problem, it has been thought best to concentrate attention on the vibrations as they manifest themselves at the free surface. The modifications which the latter introduces into the character of the waves propagated into the interior of the solid are accordingly not examined minutely.

1,000 citations