Forced Vertical Vibration of Rigid Discs with Arbitrary Embedment
Publication: Journal of Engineering Mechanics
Volume 117, Issue 11
Abstract
This paper is concerned with the investigation of the forced time‐harmonic vertical vibration of a rigid disc embedded at an arbitrary depth in a semi‐infinite medium. By virtue of transform methods, the generalized mixed boundary‐value problem is formulated as a set of dual integral equations, which, in turn, are reduced to a Fredholm equation of the second kind. With the aid of contour integration, the governing integral equation is solved numerically. Selected results for the complex compliance are presented to illustrate the various effects of embedment on the dynamic response. In addition to furnishing a unified view of the static and dynamic solutions for zero and infinite embedments, the present analysis reveals a dynamic boundary‐layer phenomenon, which is apt to be of interest to this class of problems in general.
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References
1.
Arnold, R. N., Bycroft, G. N., and Warburton, G. B. (1955). “Forced vibrations of a body on an infinite elastic solid.” J. Appl. Mech., ASME, 22, 391–400.
2.
Awajobi, A. O., and Grootenhuis, P. (1965). “Vibration of rigid bodies on semi‐infinite elastic media.” Proc. Roy. Soc., 287, A, 27–63.
3.
Boussinesq, J. (1885). “Applications des potentiels a l'etude de l'equilibre et du mouvement des solides elastiques.” Gauthier‐Villars, Paris, France (in French).
4.
Bycroft, G. N. (1956). “Forced vibrations of a rigid circular footing on a semi‐infinite elastic space and on a elastic stratum.” Phil. Trans. Roy. Soc. Lond., 248, A, (948), 327–368.
5.
Collins, W. D. (1962). “Some axially symmetric stress distributions in elastic solids containing penny‐shaped cracks. I. Cracks in an infinite solid and a thick plate.” Proc. Roy. Soc. Ser. A, 203, 359–386.
6.
Gladwell, G. M. L. (1968). “Forced tangential and rotatory vibration of a rigid circular disc on a semi‐infinite solid.” Int. J. Engrg. Sci., 6, 591–607.
7.
Harding, J. W., and Sneddon, I. N. (1945). “The elastic stresses produced by the indentation of the plane surface of a semi‐infinite elastic solid by a rigid punch.” Proc. Camb. Phil. Soc., 41, 16–26.
8.
Kassir, M. K., and Sih, G. C. (1968). “Some three‐dimensional inclusion problems in elasticity.” Int. J. Sol. Struct., 4, 225–241.
9.
Keer, L. M. (1965). “A note on the solution of two asymetric boundary value problems.” Int. J. Sol. Struct., 1, 257–264.
10.
Keer, L. M. (1967). “Mixed boundary value problems for an elastic half‐space.” Proc. Camb. Phil. Soc., 63, 1379–1386.
11.
Luco, J. E., and Westmann, R. A. (1971). “Dynamic response of circular footings.” J. Engrg. Mech., ASCE, 95(5), 1381–1194.
12.
Miklowitz, J. (1978). The theory of elastic waves and waveguides, North‐Holland Publ. Co., Amsterdam, the Netherlands.
13.
Noble, B. (1963). “The solution of Bessel function dual integral equations by a multiplying‐factor method.” Proc. Camb. Phil. Soc., 59, 351–362.
14.
Pak, R. Y. S. (1987). “Asymmetric wave propagation in an elastic half‐space by a method of potentials.” J. Appl. Mech., ASME, 121–126.
15.
Pak, R. Y. S., and Gobert, A. T. (1990). “On the axisymmetric interaction of a rigid disc embedded in a semi‐infinite solid.” Z. Angew. Math. Phys., 41, 684–700.
16.
Reissner, E., and Sagoci, H. F. (1944). “Forced torsional oscillations of an elastic half‐space, I.” J. Appl. Phys., 15(9), 652–654.
17.
Robertson, I. A. (1966). “Forced vertical vibration of a rigid circular disc on a semi‐infinite elastic solid.” Proc. Camb. Phil. Soc., 62, A, 547–553.
18.
Selvadurai, A. P. S. (1976). “The load‐deflection characteristics of a deep rigid anchor in elastic medium.” Geotechnique, 26, 601–612.
19.
Selvadurai, A. P. S. (1981). “Rotary oscillations of a rigid disc inclusion embedded in an isotropic elastic infinite space.” Int. J. Sol. Struct., 17, 492–498.
20.
Sneddon, I. N. (1966). “The Reissner‐Sagoci problem.” Proc. Glasg. Math. Assoc., 1, 136–144.
21.
Spence, D. A. (1968). “Self‐similar solutions to adhesive contact problems with incremental loading.” Proc. Roy. Soc. Lond., 305, A, 55–80.
22.
Ufliand, I. S. (1956). “Contact problems in the theory of elasticity for a circular punch in the presence of adhesion.” Prikl. Mat. Mekh., 20, 578–581.
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Published In
Journal of Engineering Mechanics
Volume 117 • Issue 11 • November 1991
Pages: 2527 - 2548
Copyright
Copyright © 1991 ASCE.
History
Published online: Nov 1, 1991
Published in print: Nov 1991
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