Summary
The boundary and the finite element formulations for the equations of elasticity are presented and applied to the problem of propagation of transient SH-waves in dipping layers overlying a half-space. When the finite element formulation is used, appropriate boundary conditions are imposed on the additional boundary dividing the half-space into a finite and an infinite region. These conditions ensure the transmission of waves across this boundary. When the boundary element method is applied, it is necessary to satisfy the radiation conditions. Theoretical seismograms for the displacement on the surface of the half-space are presented. They show that, for a specific case, the agreement between the two methods is satisfactory. The results can be compared with those found by the exact method of generalized rays in order to check the validity of the finite and the boundary element methods for the specific problem studied in this paper.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Lamb, H.: On the propagation of tremors over the surface of an elastic solid. Philos. Trans. R. Soc. LondonA 203, 1–42 (1904).
Nakano, H.: On Rayleigh waves. Japan J. Astron. Geophys.2, 233–326 (1925).
Lapwood, E. R.: The disturbance due to a line source in a semi-infinite elastic medium. Philos. Trans. R. Soc. LondonA 242, 63–100 (1949).
Garvin, W. W.: Exact transient solutions of the buried line source problem. Proc. R. Soc. LondonA 234, 528–541 (1956).
Pekeris, C. L.: The seismic surface pulse. Proc. Natl. Acad. Sci. U.S.A.41, 469–480 (1955).
Pao, Y. H., Gajewski, R. R.: The generalized ray theory and transient responses of layered elastic solid. In: Physical Acoustics, Vol.13 (Mason, W. P., Thurston, R. N., eds.) pp. 183–265. New York: Academic Press 1977.
Ziegler, F., Pao, Y. H., Wang, Y. S.: Generalized ray-integral representation of transient SH-waves in a multiply layered half-space with dipping structure. Acta Mechanica56, 1–15 (1985).
Ziegler, F., Pao, Y. H.: Theory of generalized rays for SH-waves in dipping layers. Wave Motion7, 1–24 (1985).
Lysmer, J., Waas, G.: Shear waves in plane infinite structures. J. Eng. Mech. Div.96, 85–104 (1972).
Chen, J. C., Lysmer, J., Seed, H. B.: Analysis of local variations in free-field ground motion. Report EERC3, Berkeley, California, 1981.
Wolf, J. P.: Dynamic soil-structure interaction. New York: Prentice-Hall 1985.
Brankov G., Ivanov, Ts., Angelov, T.: Numerical investigation of wave propagation in layered media. Part 1. Propagation of SH-waves. Theoretical and Applied Mechanics (Bulgaria)19, 32–41 (1988).
Hadjikov, L., Dineva, P., Rangelov, Ts.: Nonelastic soil-structure interaction by BE- and FE-methods. Transactions of the 9th Conf. on SMiRT, pp. 1149–1153, Lausanne, 17–21 August 1987.
Hadjikov, L., Dineva, P., Rangelov, Ts.: On the analysis of the dynamic soil-structure interaction by a hybrid method (SH-waves). Transactions of the Int. Conf. on Boundary Elements, pp. 469–474, China, 14–17 October 1986.
Brebia, C. A., Walker, S.: Boundary element technics in engineering. London: Butherworth 1980.
Banagh, P. P., Goldsmith, W.: Diffraction of steady acoustic waves by surface of arbitrary shape. JASA35, 1590–1601 (1963).
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Ivanov, T., Dineva, P., Angelov, T. et al. Propagation of transient SH-waves in a dipping structure by finite- and boundary element methods. Acta Mechanica 80, 113–125 (1989). https://doi.org/10.1007/BF01178183
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF01178183