Summary
The axisymmetric response of an elastic half-space to the sudden application of radial shear surface loadings is investigated in this paper. Exact expressions for the surface displacement components are developed by means of integral transforms and complex functions. Numerical results are presented in diagrams to show the wave propagation on the surface due to the dynamic loadings, and the wave front singularities in the displacement components are particularly discussed. It is found that, for a given point on the half-space surface, Rayleigh surface waves issued from the nearest and farthest disturbances give rise to a jump or a two-sided logarithmic singularity in the displacement components.
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References
Chao, C. C.: Dynamical response of an elastic half-space to tangential surface loadings. Trans. ASME Ser. E: J. Appl. Mech. 27, (1960) 559–567
Gakenheimer, D. C.; Miklowitz, J.: Transient, excitation of an elastic half-space by a point load traveling on the surface. Trans. ASME Ser. E: J. Appl. Mech. 36 (1969) 505–515
Mitra, M.: Disturbance produced in an elastic half-space by impulsive normal pressure. Proc. Cambridge Philos. Soc. 60 (1964) 683–696
Brock, L. M.: Wave propagation in an elastic half-space due to surface pressure over a non-uniformly changing circular zone. Q. Appl. Math. 38 (1980) 37–49
Eason, G.: The displacement produced in an elastic half-space by a suddenly applied surface force. J. Inst. Math. Appl. 2 (1966) 299–326
Laturelle, F. G.: The stress produced in an elastic half-space by a normal step loading over a circular area: Analytical and numerical results. Wave Motion 12 (1990) 107–127
Pekeris, C. L.: The seismic buried pulse. Proc. Nat. Acad. Sci USA 41 (1955) 629–639
Miklowitz, J.: Elastic waves and waveguides. Amsterdam: North-Holland 1978
Sneddon, I. N.: Fourier transforms. New York: McGraw-Hill 1951
Achenbach, J. D.: Wave propagation in elastic solids. Amsterdam: North-Holland 1973
Eringen, A. C.; Erdogan, S. S.: Elastodynamics, vol. II, linear theory, New York: Academic Press 1975
Abramowitz, M.; Stegun, A.: Handbook of mathematical functions. New York: Washington D.C.: US Government Print 1964
Timoshenko, S. P.; Goodier, J. N.: Theory of elasticity. New York: McGraw-Hill 1951
Gradshteyn, I. S.; Ryzhik, I. M.: Table of integrals, series, and products. New York: Academic Press 1980
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Liu, T. Dynamic response of a half-space to radial shear surface loadings. Arch. Appl. Mech. 66, 137–148 (1996). https://doi.org/10.1007/BF00795215
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DOI: https://doi.org/10.1007/BF00795215