| | | |

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

#### Nihal Ege [1] , Onur Şahin [2] , Barış Erbaş [3]

##### 21 153

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.
Moving load, Asymptotic model, Rayleigh wave, Causality
• Cole, J. and Huth, J. Stresses produced in a half plane by moving loads, J. Appl. Mech. 25, 433436, 1958.
• Freund, L. B. Wave motion in an elastic solid due to a nonuniformly moving line load, Quart. Appl. Math. 30, 271281, 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), 440451, 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), 24852496, 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), 209230, 2006.
• 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.
• 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.
• Erbaş, B. and Şahin, O. On the causality of the Rayleigh wave, Journal of Mechanics of Material and Structures 11 (4), 449461, 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), 73114.
• 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.
• 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), 15581565, 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), 768782, 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), 12291238, 2013.
• Zauderer, E. Partial dierential 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), 7380, 1976.
Primary Language en Mathematics Mathematics Author: Nihal Ege (Primary Author) Author: Onur Şahin Author: Barış Erbaş Publication Date: October 1, 2017
 Bibtex @research article { hujms445106, journal = {Hacettepe Journal of Mathematics and Statistics}, issn = {2651-477X}, eissn = {2651-477X}, address = {Hacettepe University}, year = {2017}, volume = {46}, pages = {817 - 828}, doi = {}, title = {Response of a 3D elastic half-space to a distributed moving load}, key = {cite}, author = {Ege, Nihal and Şahin, Onur and Erbaş, Barış} } 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. Retrieved from http://dergipark.org.tr/hujms/issue/38493/445106 MLA 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 46 (2017): 817-828 Chicago 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 46 (2017): 817-828 RIS TY - JOUR T1 - Response of a 3D elastic half-space to a distributed moving load AU - Nihal Ege , Onur Şahin , Barış Erbaş Y1 - 2017 PY - 2017 N1 - DO - T2 - Hacettepe Journal of Mathematics and Statistics JF - Journal JO - JOR SP - 817 EP - 828 VL - 46 IS - 5 SN - 2651-477X-2651-477X M3 - UR - Y2 - 2016 ER - EndNote %0 Hacettepe Journal of Mathematics and Statistics Response of a 3D elastic half-space to a distributed moving load %A Nihal Ege , Onur Şahin , Barış Erbaş %T Response of a 3D elastic half-space to a distributed moving load %D 2017 %J Hacettepe Journal of Mathematics and Statistics %P 2651-477X-2651-477X %V 46 %N 5 %R %U ISNAD Ege, Nihal , Şahin, Onur , Erbaş, Barış . "Response of a 3D elastic half-space to a distributed moving load". Hacettepe Journal of Mathematics and Statistics 46 / 5 (October 2017): 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. 2017; 46(5): 817-828. 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): 828-817.