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Dağılımlı hareketli yüke maruz kalmış bir elastik yarı düzlem için sınır değer problemi

Year 2025, Volume: 15 Issue: 1, 48 - 55, 22.04.2025

Onur Şahin , Gizem Kaya

Abstract

Bu çalışmada Gaussian tip dağılıma sahip bir hareketli yüke maruz kalmış bir elastik yarı düzlem için bir sınır değer problemi incelenmektedir. Problem, önceki çalışmalarda geliştirilmiş olan asimptotik model yardımıyla dalga potansiyelinin eliptik ve hiperbolik denklemleri cinsinden formüle edilmektedir. Sınırda verilmiş hiperbolik denklemin çözümü, yükün hızı ile yüzey dalgasının hızının birbiri arasındaki ilişkisine göre üç farklı durum için ayrı ayrı hesaplanmaktadır. Sınırda boyuna yer değiştirmenin ifadesi, sınır boyunca elde edilen dalga potansiyeli yardımıyla elde edilmekte ve sonra da bu yer değiştirmenin sayısal sonuçları, dağılım parametresinin farklı değerleri için verilmektedir.

Keywords

Asimptotik model elastik yarı düzlem hareketli dağılımlı yük sınır değer problemi.

References

  • Achenbach, J. 2012. Wave propagation in elastic solids. Elsevier.
  • Cao, Y., Xia, H., Li, Z. 2012. 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: 2485-2496. Doi: 10.1007/s12206-012-0630-1
  • Çelebi, E. 2006. 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. Doi: 10.1016/j.amc.2005.11.095
  • Çömez, İ. 2022. Dynamic contact problem for a viscoelastic orthotropic coated isotropic half plane. Acta Mechanica, 233(12): 5241-5253. Doi: 10.1007/s00707-022-03366-5
  • Çömez, İ., El-Borgi, S. 2023. Frictional contact problem of a coated half plane pressed by a rigid punch with coupled stress elasticity. Archive of Applied Mechanics, 93(9): 3533-3552. Doi: 10.1007/s00419-023-02452-x
  • Ege, N., Erbaş, B., Prikazchikov, DA. 2015. On the 3D Rayleigh wave field 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. Doi: 10.1002/zamm.201400211
  • Ege, N., Şahin, 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. Doi: 10.15672 /HJMS.2017.434
  • Erbaş, B., Şahin, O. 2016. On the causality of the Rayleigh wave. Journal of mechanics of materials and structures, 11(4): 449-461. Doi: 10.2140/jomms.2016.11.449
  • Erbaş, B., Kaplunov, J., Prikazchikov, DA., Şahin, O. 2017. The near-resonant regimes of a moving load in a three-dimensional problem for a coated elastic half-space. Mathematics and Mechanics of Solids, 22(1): 89-100. Doi: 10.1177/1081286514555
  • Frýba, L. 2013. Vibration of solids and structures under moving loads (Vol. 1). Springer science & business media.
  • Georgiadis, HG., Lykotrafitis, G. 2001. A method based on the Radon transform for three-dimensional elastodynamic problems of moving loads. Journal of elasticity and the physical science of solids, 65: 87-129. Doi: 10.1023/A:1016135605598
  • Graff, KF. 2012. Wave motion in elastic solids. Courier Corporation.
  • Kaplunov, J., Zakharov, A., Prikazchikov, D. 2006. Explicit models for elastic and piezoelastic surface waves. IMA journal of applied mathematics, 71(5): 768-782. Doi: 10.1093/imamat/hxl012
  • Kaplunov, J., Nolde, E., Prikazchikov, DA. 2010. A revisit to the moving load problem using an asymptotic model for the Rayleigh wave. Wave motion 47, no. 7: 440-451. Doi: 10.1016/j.wavemoti.2010.01.005
  • Kaplunov, J., Prikazchikov, DA., Erbaş, B., Şahin, O. 2013. On a 3D moving load problem for an elastic half space. Wave motion, 50(8): 1229-1238. Doi: 10.1016/j.wavemoti.2012.12.008 Liu, K., Zhang, Z., Pan, E. 2022. Dynamic response of a transversely isotropic and multilayered poroelastic medium subjected to a moving load. Soil Dynamics and Earthquake Engineering, 155: 107154. Doi: 10.1016/j.soildyn.2022.107154
  • Ouyang, H. 2011. Moving-load dynamic problems: A tutorial (with a brief overview). Mechanical Systems and Signal Processing, 25(6): 2039-2060. Doi: 10.1016/j.ymssp.2010.12.010
  • Radi, E. 2021. A loaded beam in full frictionless contact with a couple stress elastic half-plane: effects of non-standard contact conditions. International Journal of Solids and Structures, 232: 111175. Doi: 10.1016/j.ijsolstr.2021.111175
  • Şahin, O. 2021. Mixed boundary value problems for Rayleigh wave in a half‐plane with cubic anisotropy. ZAMM‐Journal of Applied Mathematics and Mechanics/Zeitschrift für Angewandte Mathematik und Mechanik, 101(8): e202000171. Doi: 10.1002/zamm.202000171
  • Vladimirov, VS. 1976. Equations of mathematical physics. Moscow Izdatel Nauka.
  • Wootton, PT., Kaplunov, J., Prikazchikov, D. 2020. A second-order asymptotic model for Rayleigh waves on a linearly elastic half plane. IMA Journal of Applied Mathematics, 85(1): 113-131. Doi: 10.1093/imamat/hxz037
  • Zhang, Z., Liu, S., Pan, E., Wang, Q. 2023. Dynamic loading in a transversely isotropic and layered elastic half-space. International Journal of Mechanical Sciences, 260: 108626. Doi: 10.1016/j.ijmecsci.2023.108626

Boundary value problem for an elastic half plane subjected to distributed moving load

Year 2025, Volume: 15 Issue: 1, 48 - 55, 22.04.2025

Onur Şahin , Gizem Kaya

Abstract

In this study, a boundary value problem for an elastic half-plane subjected to a moving load of Gaussian-type distribution is considered. The problem is formulated in terms of elliptic and hyperbolic equations of the wave potential with the help of the asymptotic model developed in previous studies. The solution of the hyperbolic equation given at the boundary is calculated separately for three different cases according to the relationship between the speed of the load and the speed of the surface wave. The expression of the longitudinal displacement at the boundary is obtained with the help of the wave potential obtained along the boundary, and then the numerical results of this displacement are presented for various values of the dispersion parameter.

Keywords

Asymptotic model elastic half plane distributed moving load boundary value problem.

References

  • Achenbach, J. 2012. Wave propagation in elastic solids. Elsevier.
  • Cao, Y., Xia, H., Li, Z. 2012. 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: 2485-2496. Doi: 10.1007/s12206-012-0630-1
  • Çelebi, E. 2006. 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. Doi: 10.1016/j.amc.2005.11.095
  • Çömez, İ. 2022. Dynamic contact problem for a viscoelastic orthotropic coated isotropic half plane. Acta Mechanica, 233(12): 5241-5253. Doi: 10.1007/s00707-022-03366-5
  • Çömez, İ., El-Borgi, S. 2023. Frictional contact problem of a coated half plane pressed by a rigid punch with coupled stress elasticity. Archive of Applied Mechanics, 93(9): 3533-3552. Doi: 10.1007/s00419-023-02452-x
  • Ege, N., Erbaş, B., Prikazchikov, DA. 2015. On the 3D Rayleigh wave field 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. Doi: 10.1002/zamm.201400211
  • Ege, N., Şahin, 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. Doi: 10.15672 /HJMS.2017.434
  • Erbaş, B., Şahin, O. 2016. On the causality of the Rayleigh wave. Journal of mechanics of materials and structures, 11(4): 449-461. Doi: 10.2140/jomms.2016.11.449
  • Erbaş, B., Kaplunov, J., Prikazchikov, DA., Şahin, O. 2017. The near-resonant regimes of a moving load in a three-dimensional problem for a coated elastic half-space. Mathematics and Mechanics of Solids, 22(1): 89-100. Doi: 10.1177/1081286514555
  • Frýba, L. 2013. Vibration of solids and structures under moving loads (Vol. 1). Springer science & business media.
  • Georgiadis, HG., Lykotrafitis, G. 2001. A method based on the Radon transform for three-dimensional elastodynamic problems of moving loads. Journal of elasticity and the physical science of solids, 65: 87-129. Doi: 10.1023/A:1016135605598
  • Graff, KF. 2012. Wave motion in elastic solids. Courier Corporation.
  • Kaplunov, J., Zakharov, A., Prikazchikov, D. 2006. Explicit models for elastic and piezoelastic surface waves. IMA journal of applied mathematics, 71(5): 768-782. Doi: 10.1093/imamat/hxl012
  • Kaplunov, J., Nolde, E., Prikazchikov, DA. 2010. A revisit to the moving load problem using an asymptotic model for the Rayleigh wave. Wave motion 47, no. 7: 440-451. Doi: 10.1016/j.wavemoti.2010.01.005
  • Kaplunov, J., Prikazchikov, DA., Erbaş, B., Şahin, O. 2013. On a 3D moving load problem for an elastic half space. Wave motion, 50(8): 1229-1238. Doi: 10.1016/j.wavemoti.2012.12.008 Liu, K., Zhang, Z., Pan, E. 2022. Dynamic response of a transversely isotropic and multilayered poroelastic medium subjected to a moving load. Soil Dynamics and Earthquake Engineering, 155: 107154. Doi: 10.1016/j.soildyn.2022.107154
  • Ouyang, H. 2011. Moving-load dynamic problems: A tutorial (with a brief overview). Mechanical Systems and Signal Processing, 25(6): 2039-2060. Doi: 10.1016/j.ymssp.2010.12.010
  • Radi, E. 2021. A loaded beam in full frictionless contact with a couple stress elastic half-plane: effects of non-standard contact conditions. International Journal of Solids and Structures, 232: 111175. Doi: 10.1016/j.ijsolstr.2021.111175
  • Şahin, O. 2021. Mixed boundary value problems for Rayleigh wave in a half‐plane with cubic anisotropy. ZAMM‐Journal of Applied Mathematics and Mechanics/Zeitschrift für Angewandte Mathematik und Mechanik, 101(8): e202000171. Doi: 10.1002/zamm.202000171
  • Vladimirov, VS. 1976. Equations of mathematical physics. Moscow Izdatel Nauka.
  • Wootton, PT., Kaplunov, J., Prikazchikov, D. 2020. A second-order asymptotic model for Rayleigh waves on a linearly elastic half plane. IMA Journal of Applied Mathematics, 85(1): 113-131. Doi: 10.1093/imamat/hxz037
  • Zhang, Z., Liu, S., Pan, E., Wang, Q. 2023. Dynamic loading in a transversely isotropic and layered elastic half-space. International Journal of Mechanical Sciences, 260: 108626. Doi: 10.1016/j.ijmecsci.2023.108626
There are 21 citations in total.

Details

Primary Language Turkish
Subjects Theoretical and Applied Mechanics in Mathematics, Applied Mathematics (Other), Continuum Mechanics
Journal Section Research Articles
Authors

Onur Şahin 0000-0001-5389-9855

Gizem Kaya 0009-0003-4532-7605

Publication Date April 22, 2025
Submission Date July 18, 2024
Acceptance Date November 11, 2024
Published in Issue Year 2025 Volume: 15 Issue: 1

Cite

APA Şahin, O., & Kaya, G. (2025). Dağılımlı hareketli yüke maruz kalmış bir elastik yarı düzlem için sınır değer problemi. Karaelmas Fen Ve Mühendislik Dergisi, 15(1), 48-55. https://doi.org/10.7212/karaelmasfen.1518481
AMA Şahin O, Kaya G. Dağılımlı hareketli yüke maruz kalmış bir elastik yarı düzlem için sınır değer problemi. Karaelmas Fen ve Mühendislik Dergisi. April 2025;15(1):48-55. doi:10.7212/karaelmasfen.1518481
Chicago Şahin, Onur, and Gizem Kaya. “Dağılımlı Hareketli yüke Maruz kalmış Bir Elastik Yarı düzlem için sınır değer Problemi”. Karaelmas Fen Ve Mühendislik Dergisi 15, no. 1 (April 2025): 48-55. https://doi.org/10.7212/karaelmasfen.1518481.
EndNote Şahin O, Kaya G (April 1, 2025) Dağılımlı hareketli yüke maruz kalmış bir elastik yarı düzlem için sınır değer problemi. Karaelmas Fen ve Mühendislik Dergisi 15 1 48–55.
IEEE O. Şahin and G. Kaya, “Dağılımlı hareketli yüke maruz kalmış bir elastik yarı düzlem için sınır değer problemi”, Karaelmas Fen ve Mühendislik Dergisi, vol. 15, no. 1, pp. 48–55, 2025, doi: 10.7212/karaelmasfen.1518481.
ISNAD Şahin, Onur - Kaya, Gizem. “Dağılımlı Hareketli yüke Maruz kalmış Bir Elastik Yarı düzlem için sınır değer Problemi”. Karaelmas Fen ve Mühendislik Dergisi 15/1 (April 2025), 48-55. https://doi.org/10.7212/karaelmasfen.1518481.
JAMA Şahin O, Kaya G. Dağılımlı hareketli yüke maruz kalmış bir elastik yarı düzlem için sınır değer problemi. Karaelmas Fen ve Mühendislik Dergisi. 2025;15:48–55.
MLA Şahin, Onur and Gizem Kaya. “Dağılımlı Hareketli yüke Maruz kalmış Bir Elastik Yarı düzlem için sınır değer Problemi”. Karaelmas Fen Ve Mühendislik Dergisi, vol. 15, no. 1, 2025, pp. 48-55, doi:10.7212/karaelmasfen.1518481.
Vancouver Şahin O, Kaya G. Dağılımlı hareketli yüke maruz kalmış bir elastik yarı düzlem için sınır değer problemi. Karaelmas Fen ve Mühendislik Dergisi. 2025;15(1):48-55.
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