Response of a 3D elastic half-space to a distributed moving load Nihal Ege∗†, Onur ahin‡ and Bar ³ Erba³

Response of a 3D elastic half-space to a distributed moving load Nihal Ege∗†, Onur ahin‡ and Bar ³ Erba³

The dynamic eect of an out of plane distributed moving load on thesurface of an elastic half-space is considered. The problem is formulatedin terms of a hyperbolic-elliptic asymptotic model for a movingload where the trajectory and the distribution of the load are taken tobe orthogonal. Steady-state equations are written in terms of a movingcoordinate system. The near-resonant solutions are, then, obtained forsub and super-Rayleigh cases taking into account the causality principle.Numerical results of displacement components are presented forvarious values of the distribution parameter.

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  • Chadwick, P. Surface and interfacial waves of arbitrary form in isotropic elastic media, J. of Elasticity 6 (1), 73-80, 1976
  • Courant, R. and Hilbert, D. Methods of Mathematical Physics (Vol. 2, John Wiley & Sons, 1989).
  • Zauderer, E. Partial dierential equations of applied mathematics (Vol. 71, John Wiley & Sons, 2011).
  • Kaplunov, J., Prikazchikov, D. A., Erba³, B. and ahin, O. On a 3D moving load problem for an elastic half space, Wave Motion 50 (8), 1229-1238, 2013.
  • Kaplunov, J., Zakharov, A. and Prikazchikov, D. A. Explicit models for elastic and piezoelastic surface waves, IMA J. Appl. Math. 71 (5), 768-782, 2006.
  • Achenbach, J. Wave propagation in elastic solids (Elsevier, 2012).
  • Ege, N., Erba³, B. and Prikazchikov, D. A. On the 3D Rayleigh wave feld on an elastic half-space subject to tangential surface loads, ZAMM-Journal of Applied Mathematics and Mechanics/Zeitschrift für Angewandte Mathematik und Mechanik 95 (12), 1558-1565, 2015.
  • Erbaş, B., Kaplunov, J., Prikazchikov, D. A. and ahin O. The near-resonant regimes of a moving load in a 3D problem for a coated elastic half space, Math. Mech. Solids DOI:10.1177/1081286514555451, 2010.
  • Dai, H. H., Kaplunov, J. and Prikazchikov, D. A. A long-wave model for the surface elastic wave in a coated half-space, Proc. R. Soc. A. 466 (2122), 3097-3116, 2010.
  • Kaplunov, J. and Prikazchikov, D. Explicit models for surface, interfacial and edge waves, in: Dynamic Localization Phenomena in Elasticity, Acoustics and Electromagnetism (Craster, R. V. and Kaplunov, J., eds.) CISM Courses and Notes, 547 (Springer, 2013), 73-114.
  • Erbaş, B. and ahin, O. On the causality of the Rayleigh wave, Journal of Mechanics of Material and Structures 11 (4), 449-461, 2016.
  • Zhu, X. Q. and Law, S. S. Dynamic load on continuous multi-lane bridge deck from moving vehicles, Journal of Sound and Vibration 251 (4), 697-716, 2002.
  • Hackenberg, M. and Müller, G. Modeling a Halfspace with Tunnel using a Coupled Integral Transform Method-Finite Element Method Approach, PAMM 15 (1), 389-390, 2015.
  • Celebi, E. Three-dimensional modelling of train-track and sub-soil analysis for surface vibrations due to moving loads, Applied Mathematics and Computation 179 (1), 209-230, 2006.
  • Cao, Y., Xia, H. and Li, Z. A semi-analytical/FEM model for predicting ground vibrations induced by high-speed train through continuous girder bridge, Journal of Mechanical Science and Technology 26 (8), 2485-2496, 2012.
  • Kaplunov, J., Nolde, E. and Prikazchikov, D. A. A revisit to the moving load problem using an asymptotic model for the Rayleigh wave, Wave Motion 47 (7), 440-451, 2010.
  • Fryba, L. Vibration of solids and structures under moving loads (Thomas Telford, London, 1999).
  • Freund, L. B. Wave motion in an elastic solid due to a nonuniformly moving line load, Quart. Appl. Math. 30, 271-281, 1972.
  • Cole, J. and Huth, J. Stresses produced in a half plane by moving loads, J. Appl. Mech. 25, 433-436, 1958.