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Year 2017, Volume: 46 Issue: 5, 817 - 828, 01.10.2017

Abstract

References

  • Cole, J. and Huth, J. Stresses produced in a half plane by moving loads, J. Appl. Mech. 25, 433436, 1958.
  • Freund, L. B. Wave motion in an elastic solid due to a nonuniformly moving line load, Quart. Appl. Math. 30, 271281, 1972.
  • Fryba, L. Vibration of solids and structures under moving loads (Thomas Telford, London, 1999).
  • 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), 440451, 2010.
  • 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), 24852496, 2012.
  • Celebi, E. Three-dimensional modelling of train-track and sub-soil analysis for surface vi- brations due to moving loads, Applied Mathematics and Computation 179 (1), 209230, 2006.
  • Hackenberg, M. and Müller, G. Modeling a Halfspace with Tunnel using a Coupled Integral Transform Method-Finite Element Method Approach, PAMM 15 (1), 389390, 2015.
  • 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), 697716, 2002.
  • Erbaş, B. and Ş“ahin, O. On the causality of the Rayleigh wave, Journal of Mechanics of Material and Structures 11 (4), 449461, 2016.
  • 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), 73114.
  • 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), 30973116, 2010.
  • 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.
  • Ege, N., Erbaş, B. and Prikazchikov, D. A. On the 3D Rayleigh wave eld 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), 15581565, 2015.
  • Achenbach, J. Wave propagation in elastic solids (Elsevier, 2012).
  • Kaplunov, J., Zakharov, A. and Prikazchikov, D. A. Explicit models for elastic and piezoe- lastic surface waves, IMA J. Appl. Math. 71 (5), 768782, 2006.
  • 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), 12291238, 2013.
  • Zauderer, E. Partial dierential equations of applied mathematics (Vol. 71, John Wiley & Sons, 2011).
  • Courant, R. and Hilbert, D. Methods of Mathematical Physics (Vol. 2, John Wiley & Sons, 1989).
  • Chadwick, P. Surface and interfacial waves of arbitrary form in isotropic elastic media, J. of Elasticity 6 (1), 7380, 1976.

Response of a 3D elastic half-space to a distributed moving load

Year 2017, Volume: 46 Issue: 5, 817 - 828, 01.10.2017

Abstract

The dynamic effect of an out of plane distributed moving load on the surface of an elastic half-space is considered. The problem is formulated
in terms of a hyperbolic-elliptic asymptotic model for a moving load where the trajectory and the distribution of the load are taken to be orthogonal. Steady-state equations are written in terms of a moving coordinate system. The near-resonant solutions are, then, obtained for
sub and super-Rayleigh cases taking into account the causality principle. Numerical results of displacement components are presented for
various values of the distribution parameter.

References

  • Cole, J. and Huth, J. Stresses produced in a half plane by moving loads, J. Appl. Mech. 25, 433436, 1958.
  • Freund, L. B. Wave motion in an elastic solid due to a nonuniformly moving line load, Quart. Appl. Math. 30, 271281, 1972.
  • Fryba, L. Vibration of solids and structures under moving loads (Thomas Telford, London, 1999).
  • 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), 440451, 2010.
  • 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), 24852496, 2012.
  • Celebi, E. Three-dimensional modelling of train-track and sub-soil analysis for surface vi- brations due to moving loads, Applied Mathematics and Computation 179 (1), 209230, 2006.
  • Hackenberg, M. and Müller, G. Modeling a Halfspace with Tunnel using a Coupled Integral Transform Method-Finite Element Method Approach, PAMM 15 (1), 389390, 2015.
  • 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), 697716, 2002.
  • Erbaş, B. and Ş“ahin, O. On the causality of the Rayleigh wave, Journal of Mechanics of Material and Structures 11 (4), 449461, 2016.
  • 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), 73114.
  • 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), 30973116, 2010.
  • 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.
  • Ege, N., Erbaş, B. and Prikazchikov, D. A. On the 3D Rayleigh wave eld 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), 15581565, 2015.
  • Achenbach, J. Wave propagation in elastic solids (Elsevier, 2012).
  • Kaplunov, J., Zakharov, A. and Prikazchikov, D. A. Explicit models for elastic and piezoe- lastic surface waves, IMA J. Appl. Math. 71 (5), 768782, 2006.
  • 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), 12291238, 2013.
  • Zauderer, E. Partial dierential equations of applied mathematics (Vol. 71, John Wiley & Sons, 2011).
  • Courant, R. and Hilbert, D. Methods of Mathematical Physics (Vol. 2, John Wiley & Sons, 1989).
  • Chadwick, P. Surface and interfacial waves of arbitrary form in isotropic elastic media, J. of Elasticity 6 (1), 7380, 1976.
There are 19 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Mathematics
Authors

Nihal Ege

Onur Ş“ahin

Barış Erbaş This is me

Publication Date October 1, 2017
Published in Issue Year 2017 Volume: 46 Issue: 5

Cite

APA Ege, N., Ş“ahin, O., & Erbaş, B. (2017). Response of a 3D elastic half-space to a distributed moving load. Hacettepe Journal of Mathematics and Statistics, 46(5), 817-828.
AMA Ege N, Ş“ahin O, Erbaş B. Response of a 3D elastic half-space to a distributed moving load. Hacettepe Journal of Mathematics and Statistics. October 2017;46(5):817-828.
Chicago Ege, Nihal, Onur Ş“ahin, and Barış Erbaş. “Response of a 3D Elastic Half-Space to a Distributed Moving Load”. Hacettepe Journal of Mathematics and Statistics 46, no. 5 (October 2017): 817-28.
EndNote Ege N, Ş“ahin O, Erbaş B (October 1, 2017) Response of a 3D elastic half-space to a distributed moving load. Hacettepe Journal of Mathematics and Statistics 46 5 817–828.
IEEE N. Ege, O. Ş“ahin, and B. Erbaş, “Response of a 3D elastic half-space to a distributed moving load”, Hacettepe Journal of Mathematics and Statistics, vol. 46, no. 5, pp. 817–828, 2017.
ISNAD Ege, Nihal et al. “Response of a 3D Elastic Half-Space to a Distributed Moving Load”. Hacettepe Journal of Mathematics and Statistics 46/5 (October 2017), 817-828.
JAMA Ege N, Ş“ahin O, Erbaş B. Response of a 3D elastic half-space to a distributed moving load. Hacettepe Journal of Mathematics and Statistics. 2017;46:817–828.
MLA Ege, Nihal et al. “Response of a 3D Elastic Half-Space to a Distributed Moving Load”. Hacettepe Journal of Mathematics and Statistics, vol. 46, no. 5, 2017, pp. 817-28.
Vancouver Ege N, Ş“ahin O, Erbaş B. Response of a 3D elastic half-space to a distributed moving load. Hacettepe Journal of Mathematics and Statistics. 2017;46(5):817-28.