A Potential Method for Body and Surface Wave Propagation in Transversely Isotropic Half- and Full-Spaces

Document Type : Research Papers

Authors

1 K. N. Toosi University of technology, Faculty of Geodesy and Geomatics.

2 University of Tehran, Faculty of Civil Engineering.

Abstract

The problem of propagation of plane wave including body and surface waves propagating in a transversely isotropic half-space with a depth-wise axis of material symmetry is investigated in details. Using the advantage of representation of displacement fields in terms of two complete scalar potential functions, the coupled equations of motion are uncoupled and reduced to two independent equations for potential functions. In this paper, the secular equations for determination of body and surface wave velocities are derived in terms of both elasticity coefficients and the direction of propagation. In particular, the longitudinal, transverse and Rayleigh wave velocities are determined in explicit forms. It is also shown that in transversely isotropic materials, a Rayleigh wave may propagate in different manner from that of isotropic materials. Some numerical results for synthetic transversely isotropic materials are also illustrated to show the behavior of wave motion due to anisotropic nature of the problem.

Keywords

Main Subjects

References

Amiri-Hezaveh, A., Eskandari-Ghadi, M., Rahimian, M. and Gharbani-Tanha, A.K. (2013). “Impedance functions for surface rigid rectangular foundations on transversely isotropic multilayer half-spaces”, Journal of Applied Mechanics, 80(5), 051017-1 to 051017-12.
Ardeshir-Behrestaghi, A., Eskandari-Ghadi, M. (2010). “Semi-analytic method for a tri-material transversely isotropic full-space in frequency domain”, Journal of Civil and Surveying Engineering, 44(1), 13-25.
 Ardeshir-Behrestaghi, A., Eskandari-Ghadi, M., and Vaseghi-Amiri, J. (2013). “Analytical solution for a two-layer transversely isotropic half-space affected by an Arbitrary shape dynamic surface load”, Civil Engineering Infrastructures Journal, 46(1), 1-14.
Chadwick, P. (1988). “Wave propagation in transversely isotropic elastic media. I. homogenous plane wave”, Proceeding of Royal Society of London A, 422, 23-66.
Chadwick, P. (1989). “Wave propagation in transversely isotropic elastic media, II: Surface waves”, Proceeding of Royal Society of London A, 422, 67-101
Eskandari-Ghadi, M. (2005). “A complete solution of the wave equations for transversely isotropic media”, Journal of Elasticity, 81(1), 1-19.
Eskandari-Ghadi, M. and Sattar, S. (2009), “Axisymmetric transient waves in transversely isotropic half-space”, Soil Dynamics and Earthquake Engineering, 29(2), 347-355.
Eskandari-Ghadi, M., Ardeshir-Begrestaghi, A. (2011). “Elastodynamic scalar potential functions in cylindrical coordinate systems”, Journal of Civil and Surveying Engineering, 45(2), 125-266.
Eskandari-Ghadi, M., Fallahi, M. and Ardeshir-Behrestaghi, A. (2010). “Forced vertical vibration of rigid circular disc on a transversely isotropic half-space”, Journal of Engineering Mechanics, 136(7), 913-922.
 Eskandari-Ghadi, M., Hassanpour-Chermahini, A. and Ardeshir-Behrestaghi, A. (2014). “A method of function space for vertical impedance function of a circular rigid foundation on a transversely isotropic ground”, Civil Engineering Infrastructures Journal, 47(1), 13-27.
Eskandari-Ghadi, M., Mirzapour, A. and Ardeshir-Behrestaghi, A. (2011). “Rocking vibration of rigid circular disc in a transversely isotropic full-space”, Journal of Numerical Analytical Methods in. Geomechanics, 35(14), 1587-1603
Eskandari-Ghadi, M., Mirzapour, M. and Ardeshir-Behrestaghi, A. (2012). “Interaction of rocking vibration of a buried rigid circular disc and a two-layer transversely isotropic half-space”, Scientia Iranica, 20(1), 1-14.
Graff, K.F. (1991). Wave motion in elastic solids, Dover Publication Inc, New York.
Hu, H.C. (1953). “On the three dimensional problems of the theory of elasticity of a transversely isotropic body”, Scientia Sinica Mathematica, 2, 145-151. 
Kirkner, J. (1982). “Vibration of a rigid disc on a transversely isotropic elastic half space”, Journal of Numerical and Analytical Method in Geomechanics, 6(3), 293-306.
Lekhnitskii, S. G. (1981). Theory of anisotropic elastic bodies, Holden-Day Publishing Co, San Francisco, California.
Miklowitz, J. (1978). Theory of elastic waves and waveguides, North-Holland Publishing Company, Amsterdam.
Raoofian Naeeni, M., Eskandari-Ghadi, M., Ardalan, A. A., Sture, S. and Rahimian, M. (2015a). “Transient response of a thermoelastic half-space to mechanical and thermal buried sources”, Journal of Applied Mathematics and Mechanics (ZAMM), 95(4), 354-376.
Raoofian Naeeni, M., Eskandari-Ghadi, M., Ardalan, A. A., Pak, R. Y. S., Rahimian, M. and Hayati, Y. (2015b). “Coupled thermo-viscoelasto-dynamic Green's functions for bi-material half space”, Journal of Applied Mathematics and Mechanics (ZAMM), 95(3), 260-282.
Raoofian Naeeni, M. and Eskandari-Ghadi, M. (2016). “Analytical solution of the asymmetric transient wave in a transversely isotropic half-space due to both buried and surface impulses”, Soil Dynamics and Earthquake Engineering, 81, 42-57.
Slawinski, M.A. (2010). Waves and rays in elastic continua, World Scientific, ISBN: 978-981-4289-00-9
Sternberg E. and Gurtin, M.E. (1962), “On the completeness of certain stress functions in the linear theory of elasticity”, Proceedings of the fourth U.S. National Congress of Applied Mechanics, Technical Report, Brown University, 12, 793-797,
Stoneley, R. (1949). “The seismological implications of aelotropy in continental structures”, Royal Astronomical Society Monthly Notices, Geophysical Supplement, London, England, 5(8), 343-353.
Civil Engineering Infrastructures Journal
Volume 49, Issue 2
December 2016
Pages 263-288

Files

History

  • Receive Date: 11 February 2016
  • Revise Date: 14 September 2016
  • Accept Date: 19 September 2016

Share

How to cite

Statistics