Forced Horizontal Vibration of Rigid Disc in Transversely Isotropic Trimaterial Full-Space
Publication: Journal of Engineering Mechanics
Volume 143, Issue 3
Abstract
A theoretical investigation is presented for the dynamic interaction of a rigid circular disc and its surrounding space, which is a trimaterial transversely isotropic full-space, and the disc is undergoing a prescribed horizontal harmonic vibration. Because the equations of motion form a system of coupled partial differential equations in a cylindrical coordinate system, a system of two scalar potential functions are used to decouple the equations of motion. This approach results in a set of two separated partial differential equations, which may be transformed to some ordinary differential equations by using Fourier series along the angular coordinate and the Hankel integral transformations with respect to the radial coordinate in a cylindrical coordinate system. After solving the ordinary differential equations, the unknown functions are determined by satisfying relaxed boundary conditions, which themselves are transformed to a set of four coupled integral equations. These coupled integral equations are reduced to two coupled Fredholm-Volterra integral equations of the second kind, which are numerically solved in this paper. The proposed solutions are applied for a transversely isotropic half-space, and the results showed the conformation of the existing solutions.
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References
Boussinesq, J. (1885). Applications des potentiels à l’étude de l’équilibre et du mouvement des solides élastiques, Gauthier-Villaars, Paris (in French).
Bycroft, G. N. (1956). “Forced vibrations of a rigid circular footing on a semi-infinite elastic space and on an elastic stratum.” Phil. Trans. R. Soc. London A, 248(948), 327–368.
Collins, W. D. (1962). “Some axially symmetric stress distribution in elastic solids containing penny-shaped cracks. I: Cracks in an infinite solid and a thick plate.” Proc. R. Soc. London A, 266(1326), 359–386.
Eskandari-Ghadi, M. (2005). “A complete solution of the wave equations for transversely isotropic media.” J. Elast., 81(1), 1–19.
Eskandari-Ghadi, M., Fallahi, M., and Ardeshir-Behrestaghi, A. (2014a). “A forced vertical vibration of rigid circular disc on a transversely isotropic half-space.” J. Eng. Mech., 913–922.
Eskandari-Ghadi, M., Nabizadeh, S. M., and Ardeshir-Behrestaghi, A. (2014b). “Vertical and horizontal vibration of a rigid disc on a multi-layered transversely isotropic half-space.” Soil Dyn. Earthquake Eng., 61–62, 135–139.
Eskandari-Ghadi, M., Pak, R. Y. S., and Ardeshir-Behrestaghi, A. (2008). “Transversely isotropic elastodynamic solution of a finite layer on an infinite subgrade under surface loads.” Soil Dyn. Earthquake Eng., 28(12), 986–1003.
Eskandari-Ghadi, M., Sture, S., Pak, R. Y. S., and Ardeshir-Behrestaghi, A. (2009). “A tri-material elastodynamic solution for a transversely isotropic full-space.” Int. J. Solids Struct., 46(5), 1121–1133.
Gladwell, G. M. L. (1968). “Forced tangential and rotatory vibration of a rigid circular disc on a semi-infinite solid.” Int. J. Eng. Sci., 6(10), 591–607.
Kassir, M. K., and Sih, G. C. (1968). “Some three-dimensional inclusion problems in elasticity.” Int. J. Solids Struct., 4(2), 225–241.
Keer, L. M. (1965). “A note on the solution of two asymmetric boundary value problems.” Int. J. Solids Struct., 1(3), 257–264.
Khojasteh, A., Rahimian, M., and Eskandari, M. (2013). “Three-dimensional dynamic green’s functions in transversely isotropic tri-materials.” Appl. Math. Modell., 37(5), 3164–3180.
Lekhnitskii, S. G. (1981). Theory of elasticity of an anisotropic body, MIR Publishers, Moscow.
Moghaddasi, H., Rahimian, M., and Khojasteh, A. (2012a). “Horizontal vibration of rigid circular foundation on a transversely isotropic half-space.” Int. J. Eng. Technol., 4(4), 400–403.
Moghaddasi, H., Rahimian, M., Khojasteh, A., and Pak, R. Y. S. (2012b). “Asymmetric interaction of a rigid disc with a transversely isotropic half-space.” Q. J. Mech. Appl. Math., 65(4), 513–533.
Noble, B. (1963). “The solution of Bessel function dual integral equations by a multiplying-factor method.” Math. Proc. Cambridge Philos. Soc., 59(2), 351–362.
Payton, R. G. (1983). Elastic wave propagation in transversely isotropic media, Martinus Nijhoff, Hague, Netherlands.
Rahimian, M., Ghorbani-Tanha, A. K., and Eskandari-Ghadi, M. (2006). “The Reissner-Sagoci problem for a transversely isotropic half-space.” Int. J. Numer. Anal. Methods Geomech., 30(11), 1063–1074.
Reissner, E., and Sagoci, H. F. (1944). “Forced torsional oscillations of an elastic half-space.” J Appl. Phys., 15(9), 652–654.
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Published In
Journal of Engineering Mechanics
Volume 143 • Issue 3 • March 2017
Copyright
© 2016 American Society of Civil Engineers.
History
Received: Dec 28, 2014
Accepted: May 20, 2016
Published online: Jul 15, 2016
Discussion open until: Dec 15, 2016
Published in print: Mar 1, 2017
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