Wave propagation in an elastic half-space due to surface pressure over a non-uniformly changing circular zone

Author:
L. M. Brock

Journal:
Quart. Appl. Math. **38** (1980), 37-49

MSC:
Primary 73D99

DOI:
https://doi.org/10.1090/qam/575831

MathSciNet review:
575831

Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: Two problems of pressure distributions applied to an elastic half-space over a circular pressure zone whose center is fixed but whose radius changes non-uniformly with time are considered. In one case, the pressure depends only on time; in the other case, the pressure varies with the radial distance from the pressure zone center. Complete transform solutions are obtained and several wave propagation aspects are briefly studied, with emphasis on the Rayleigh pole contributions and the associated propagating singularities. The effects of some specific zone time-histories on the Rayleigh pole disturbances at the half-space surface are considered. Some characteristics of a given time-history appear to be manifested in the corresponding disturbance.

**[1]**H. Lamb, Phil. Trans. Roy. Soc. (London)**A203**, 1 (1904)**[2]**C. L. Pekeris,*The seismic surface pulse*, Proc. Nat. Acad. Sci. U.S.A.**41**(1955), 469–480. MR**0072002****[3]**C. C. Chao, H. H. Bleich, and J. Sackman,*Surface waves in an elastic half space*, Trans. ASME Ser. E. J. Appl. Mech.**28**(1961), 300–301. MR**0122148****[4]**J. W. Craggs,*On axially symmetric waves. III. Elastic waves in a half-space*, Proc. Cambridge Philos. Soc.**59**(1963), 803–809. MR**0154478****[5]**C. Atkinson, Int. J. Engng. Sci.**6**, 27 (1968)**[6]**D. C. Gakenheimer, J. Appl. Mech.**38**, 99 (1971)**[7]**J. W. Miles,*On the response of an elastic half-space to a moving blast wave*, J. Appl. Mech.**27**(1960), 710–716. MR**0118082****[8]**M. L. Baron and R. Check, J. EMD, Proc. ASCE,**87**, 33 (1961)**[9]**C. M. Ablow, in*Proc. 4th U.S. Natl. Cong. Appl. Mech.*, 51 (1962)**[10]**R. M. Blowers, J. Inst. Math. Appl.,**5**, 167 (1969)**[11]**K. J. Tong,*Dynamic response of a homogeneous isotropic elastic half-space to a spreading blast wave*, Ph.D. Thesis, Stanford Univ., Stanford, California, Dec. 1968**[12]**L. B. Freund, Quart. Appl. Math.**30**, 271 (1972)**[13]**L. B. Freund, J. Appl. Mech.**40**, 699 (1973)**[14]**I. N. Sneddon,*The use of integral transforms*, McGraw-Hill, New York, 1972, Chs. 3, 5, 9**[15]**A. T. de Hoop, Appl. Sci. Res.**B8**, 349 (1960)**[16]**G. N. Watson,*A treatise on the theory of Bessel functions*, Cambridge Mathematical Library, Cambridge University Press, Cambridge, 1995. Reprint of the second (1944) edition. MR**1349110****[17]**I. S. Gradshteyn and I. M. Ryzhik,*Table of integrals, series, and products*, 6th ed., Academic Press, Inc., San Diego, CA, 2000. Translated from the Russian; Translation edited and with a preface by Alan Jeffrey and Daniel Zwillinger. MR**1773820****[18]**J. D. Achenbach,*Wave propagation in elastic solids*, North-Holland, Amsterdam, 1973, 320

Retrieve articles in *Quarterly of Applied Mathematics*
with MSC:
73D99

Retrieve articles in all journals with MSC: 73D99

Additional Information

DOI:
https://doi.org/10.1090/qam/575831

Article copyright:
© Copyright 1980
American Mathematical Society