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Research Papers

Surface Waves on a Half-Space Due to a Time-Harmonic Loading on an Inertial Strip Foundation

[+] Author and Article Information
M. Dehestani

Assistant Professor
Faculty of Civil Engineering,
Babol University of Technology, Box 484,
Babol 47148-71167, Iran
e-mail: dehestani@gmail.com

A. Vafai

Professor
Department of Civil Engineering,
Sharif University of Technology,
Tehran 11365-11155, Iran
e-mail: vafai@sharif.edu

A. J. Choobbasti

Associate Professor
Department of Civil Engineering,
Babol University of Technology, Box 484,
Babol 47148-71167, Iran
e-mail: asskar@nit.ac.ir

N. R. Malidarreh

Lecturer
Department of Civil Engineering,
Islamic Azad University,
Mahmoodabad Branch,
Mahmoodabad 47187-66941, Iran
e-mail: nimaran@gmail.com

F. Szidarovszky

Professor
Systems and Industrial Engineering Department,
University of Arizona, P.O. Box 210011,
Tucson, AZ 85721-0011
e-mail: szidar@sie.arizona.edu

1Corresponding author.

Contributed by the Noise Control and Acoustics Division of ASME for publication in the Journal of Vibration and Acoustics. Manuscript received September 5, 2011; final manuscript received February 25, 2013; published online June 18, 2013. Assoc. Editor: Liang-Wu Cai.

J. Vib. Acoust 135(5), 051008 (Jun 18, 2013) (10 pages) Paper No: VIB-11-1197; doi: 10.1115/1.4023990 History: Received September 05, 2011; Revised February 25, 2013

An analytical approach has been applied to obtain the solution of Navier's equation for a homogeneous, isotropic half-space under an inertial foundation subjected to a time-harmonic loading. Displacement potentials were used to change the Navier's equation to a system of wave-type equations. Calculus of variation was employed to demonstrate the contribution of the foundation's inertial effects as boundary conditions. Use of the Fourier transformation method for the system of Poisson-type equations and applying the boundary conditions yielded the transformed surface displacement field. Direct contour integration has been employed to achieve the surface waves. In order to clarify the foundation's inertial effects, related coefficients were defined and a parametric study was conducted. Final results revealed that increasing the mass per unit length of the foundation or the frequency of the applied harmonic load intensifies the inertial effect factors. On the other hand, an increase in strip width or Poisson's ratio would imply reduction in the inertial effect factors.

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References

Lamb, H., 1904, “On the Propagation of Tremors Over the Surface of an Elastic Solid,” Philos. Trans. R. Soc. London, Ser. A, 203, pp. 1–42. [CrossRef]
Miller, G. F., and Pursey, H., 1954, “The Field and Radiation Impedance of Mechanical Radiators on the Free Surface of a Semi-Infinite Isotropic Solid,” Proc. R. Soc. London, Ser. A, 223(1155), pp. 521–541. [CrossRef]
Pan, Y., and Chou, T., 1979, “Green's Function Solutions for Semi-Infinite Transversely Isotropic Materials,” Int. J. Eng. Sci., 17, pp. 545–551. [CrossRef]
Eskandari-Ghadi, M., Pak, R. Y. S., and Ardeshir-Behrestaghi, A., 2009, “Elastostatic Green's Functions for an Arbitrary Internal Load in a Transversely Isotropic Bi-Material Full-Space,” Int. J. Eng. Sci., 47, pp. 631–641. [CrossRef]
Khojasteh, A., Rahimiana, M., Eskandari, M., and Pak, R. Y. S., 2008, “Asymmetric Wave Propagation in a Transversely Isotropic Half-Space in Displacement Potentials,” Int. J. Eng. Sci., 46, pp. 690–710. [CrossRef]
Guangyu, L., and Kaixin, L., 2007, “Exact Solution for a Two-Dimensional Lamb's Problem Due to a Strip Impulse Loading,” Acta Mech. Solida Sinica, 20(3), pp. 258–265. [CrossRef]
Dehestani, M., Vafai, A., and Mofid, M., 2010, “Steady-State Stresses in a Half-Space Due to Moving Wheel-Type Loads With Finite Contact Patch,” Sci. Iran., Trans. A: Civil Eng., 17(5), pp. 387–395.
Bilello, C., Bergman, L. A., and Kuchma, D., 2004, “Experimental Investigation of a Small-Scale Bridge Model Under a Moving Mass,” ASCE J. Struct. Eng., 130(5), pp. 799–804. [CrossRef]
Akin, J. E., and Mofid, M., 1989, “Numerical Solution for Response of Beams With Moving Mass,” ASCE J. Struct. Eng., 115(1), pp. 120–131. [CrossRef]
Shadnam, M. R., Mofid, M., and Akin, J. E., 2001, “On the Dynamic Response of Rectangular Plate, With Moving Mass,” Thin-Walled Struct., 39, pp. 797–806. [CrossRef]
Dehestani, M., Vafai, A., and Mofid, M., 2010, “Stresses in Thin-Walled Beams Subjected to a Traversing Mass Under a Pulsating Force,” Proc. Inst. Mech. Eng., Part, C: J. Mech. Eng. Sci., 224(11), pp. 2363–2372. [CrossRef]
Rades, M., 1972, “Dynamic Analysis of an Inertial Foundation Model,” Int. J. Solids Struct., 8, pp. 1353–1372. [CrossRef]
Karabalis, D. L., and Huang, C.-F. D., 1991, “Inertial Soil-Foundation Interaction by a Direct Time Domain BEM,” Math. Comput. Modell., 15(3–5), pp. 215–228. [CrossRef]
Guenfoud, S., Bosakov, S. V., and Laefer, D. F., 2009, “Dynamic Analysis of a Beam Resting on an Elastic Half-Space With Inertial Properties,” Soil Dyn. Earthquake Eng., 29, pp. 1198–1207. [CrossRef]
Guenfoud, S., Amrane, M. N., Bosakov, S. V., and Ouelaa, N., 2009, “Semi-Analytical Evaluation of Integral Forms Associated With Lamb's Problem,” Soil Dyn. Earthquake Eng., 29, pp. 438–443. [CrossRef]
Achenbach, J. D., 1973, Wave Propagation in Elastic Solids, North-Holland, Amsterdam.
Dehestani, M., Mofid, M., and Vafai, A., 2009, “Investigation of Critical Influential Speed for Moving Mass Problems on Beams,” Appl. Math. Modell., 33, pp. 3885–3895. [CrossRef]
Carrier, G. F., Krook, M., and Pearson, C. E., 2005, Functions of a Complex Variable: Theory and Technique, Society for Industrial and Applied Mathematics, New York.
Erdelyi, A., 1956, Asymptotic Expansions, Dover, New York.

Figures

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Fig. 1

Simulation of a strip foundation under dynamic loading

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Fig. 4

Imaginary part of J(α) with respect to α with varying values of k

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Fig. 3

Real part of J(α) with respect to α with varying values of k

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Fig. 2

Contours of integration

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Fig. 5

Variation of CIE with respect to Cm and k with α = 10

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Fig. 6

Variation of θIE with respect to Cm and k with α = 10

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Fig. 7

Variation of CIE with respect to Cm and α with k = 2

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Fig. 8

Variation of θIE with respect to Cm and α with k = 2

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Fig. 9

Variation of CIE with respect to α and k with Cm = 1

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Fig. 10

Variation of θIE with respect to α and k with Cm = 1

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