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Solutions for Triangularly Distributed Harmonic Loadings on Axially Symmetric Area in Layered Half-Space

  • G.-S. Liou (a1)


The paper is to solve the problem of the response of stratified half-space subjected to triangularly distributed time-harmonic loadings on an axial symmetric area in the stratified half-space. Since the distributed area can be very small, the solution can be employed to deal with the problems of elastodynamics using the fundamental solution method. The advantage of the presented solution over Green function is that no singularity will occur in the presented solution. Some numerical results are given and some conclusions have been made. The presented solution is very efficient in computation.


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1.Woods, R. D. and Jedele, L. P., “Energy-Attenuation Relationships from Construction Vibrations,Proceedings of Vibration Problems in Geotechnical Engineering Convention, Detroit, Michigan, pp. 229246 (1985).
2.Sheng, X., Jones, C. J. C., and Petyt, M., “Ground Vibration Generated by a Load Moving Along a Railway Track,Journal of Sound and Vibration, 228, pp. 129156 (1999).
3.Krylov, V. V., “Vibrational Impact of High-Speed Trains. I. Effect of Track Dynamics,Journal of the Acoustical Society of America, 100, pp. 31213134 (1996).
4.Kaynia, A. M., Madshus, C. and Zackrisson, P., “Ground Vibration from High-Speed Trains: Prediction and Countermeasure,Journal of Geotechnical and Geoenvironmental Engineering, 126, pp. 05310573 (2000).
5.Anders, Karlstrom, “An Analytical Model for Ground Vibrations from Accelerating Trains,Journal of Sound and Vibration, 293, pp. 587598 (2006).
6.Apsel, R. J. and Luco, J. E., “On the Green’s Functions for a Layered Half-Space, Part II,Bulletin of Seismo-logical Society of America, 73, pp. 931951 (1983).
7.Vostroukhov, A. V., Verichev, S. N., Kok, A. W. M., and Esveld, C., “Steady-State Response of a Stratified Half-Space Subjected to a Horizontal Arbitrary Buried Uniform Load Appied at a Circular Area,Soil Dynamics and Earthquake Engineering, 24, pp. 449459 (2004).
8.Kausel, E. and Peek, R., “Dynamic Loads in the Interior of a Layered Stratum: An Explicit Solution,Bulletin of the Seismological Society of America, 72, pp. 14591481 (1982).
9.Liou, G.-S., “Analytical Solutions for Soil-Structure Interaction in Layered Media,Journal of Earthquake Engineering and Structural Dynamics, 18, pp. 667686 (1989).
10.Liou, G.-S., “Vibrations Induced by Harmonic Loadings Applied at Circular Rigid Plate on HalfSpace Medium,Journal of Sound and Vibration, 323, pp. 257269 (2009).
11.Liou, G.-S., “Vibrations Induced by Harmonic Loadings Applied at Circular Plate on Layered Medium,Journal of Mechanics, 29, pp. 197206 (2013).



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