Year 2017,
Volume: 46 Issue: 5, 817 - 828, 01.10.2017
Nihal Ege
,
Onur Şahin
,
Barış Erbaş
References
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433436, 1958.
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Quart. Appl. Math. 30, 271281, 1972.
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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.
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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 Şahin, 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
Nihal Ege
,
Onur Şahin
,
Barış Erbaş
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 Şahin, 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.