Dynamic response of an elastic half-space to time-dependent surface tractions over an embedded spherical cavity

Thiruvenkatachar, V. R.; Viswanathan, K. K.

doi:10.1098/rspa.1965.0196

Cited by 16 publications

(3 citation statements)

References 2 publications

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“…The numerical calculation is carried out for two different cases of cavity non-expansion and cavity expansion velocity constants. Thiruvenkatachar derived the series form the transient solution of the semi-infinite elastic space problem using the iterative method (Thiruvenkatachar and Viswanathan, 1965) and proved its convergence. Considering the complexity of the series solution, the analytical approximation (Thiruvenkatachar and Viswanathan, 1967) was made on the steady-state solution using the saddle-point method, and the approximate solution of three emissions between the chamber wall and the free surface is obtained.…”

Section: Introductionmentioning

confidence: 99%

“…Thiruvenkatachar derived the series form the transient solution of the semi-infinite elastic space problem using the iterative method (Thiruvenkatachar and Viswanathan, 1965) and proved its convergence. Considering the complexity of the series solution, the analytical approximation (Thiruvenkatachar and Viswanathan, 1967) was made on the steady-state solution using the saddle-point method, and the approximate solution of three emissions between the chamber wall and the free surface is obtained. At the same time, the transient solution is also calculated for the case where the pressure load on the chamber wall is subjected to an…”

Section: Introductionmentioning

confidence: 99%

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Research on the evolution law of the seismic wave field based on the explosive source parameters

Shi

Gao

et al. 2023

Front. Earth Sci.

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We present a numerical model for blast-induced seismic waves. This model is based on the transformation mechanism of the seismic wave field, and the process of the seismic wave’s generation is divided into two stages. The first stage is the generation of elastic waves. Due to the plastic deformation of the geotechnical medium in this stage, we have established the Euler model to describe it. The second stage is the prorogation of the elastic waves; we have established the Lagrange models to describe this stage. Finally, the influence of the main parameters of the explosive sources (detonation pressure and expansion index) on the seismic wave is analyzed by the established model. The results show that the proposed model in this paper can reasonably predict the evolution law of the seismic wave field based on the explosive source parameters.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Research on the evolution law of the seismic wave field based on the explosive source parameters

Shi

Gao

et al. 2023

Front. Earth Sci.

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“…The authors presume that this limitation is mainly due to difficulties in satisfying the boundary conditions at the free surface of the half-space. Thiruvenkatachar and Viswanathan [5] investigated the dynamic response of an elastic half-space with a cylindrical cavity at a finite depth subjected to time-dependent surface tractions on the boundary of the cavity. The solution was obtained by expanding the field in a series of wave functions and applying the method of successive approximations.…”

Section: Introductionmentioning

confidence: 99%

Dynamic Stress and Displacement in an Elastic Half-Space with a Cylindrical Cavity

Coşkun

Engin

Özmutlu

2011

Shock and Vibration

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Abstract. The dynamic response of an elastic half-space with a cylindrical cavity in a circular cross-section is analyzed. The cavity is assumed to be infinitely long, lying parallel to the plane-free surface of the medium at a finite depth and subjected to a uniformly distributed harmonic pressure at the inner surface. The problem considered is one of plain strain, in which it is assumed that the geometry and material properties of the medium and the forcing function are constant along the axis of the cavity. The equations of motion are reduced to two wave equations in polar coordinates with the use of Helmholtz potentials. The method of wave function expansion is used to construct the displacement fields in terms of the potentials. The boundary conditions at the surface of the cavity are satisfied exactly, and they are satisfied approximately at the free surface of the half-space. Thus, the unknown coefficients in the expansions are obtained from the treatment of boundary conditions using a collocation least-square scheme. Numerical results, which are presented in the figures, show that the wave number (i.e., the frequency) and depth of the cavity significantly affect the displacement and stress.

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A spherical wave in a viscoelastic half-space

Семенов¹

1977

J Appl Mech Tech Phys

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Dynamic response of an elastic half-space to time-dependent surface tractions over an embedded spherical cavity

Cited by 16 publications

References 2 publications

Research on the evolution law of the seismic wave field based on the explosive source parameters

Research on the evolution law of the seismic wave field based on the explosive source parameters

Dynamic Stress and Displacement in an Elastic Half-Space with a Cylindrical Cavity

A spherical wave in a viscoelastic half-space

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