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Journals / Karaelmas Fen ve Mühendislik Dergisi / 2025 / Cilt: 15 Sayı: 1

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

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

Onur Şahin(GİRESUN ÜNİVERSİTESİ)0000-0001-5389-9855
Gizem Kaya(GİRESUN ÜNİVERSİTESİ, FEN BİLİMLERİ ENSTİTÜSÜ)0009-0003-4532-7605
Pages
48–55
Publication Date
2025-04-22
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AI Summary & Key Takeaways

AI Insight
⚡ TL;DR(Too Long; Didn't Read)

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.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:In this study, a boundary value problem for an elastic half-plane subjected to a moving load of Gaussian-type distribution is considered.
📊
Key Findings & Data: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.
💡
Conclusion & Impact: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.
🔬Design:Modeling & Simulation
📍Scope:Comprehensive Sample
⚙️Variables:Asimptotik model · elastik yarı düzlem · hareketli dağılımlı yük

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.

Özet

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.

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Cite This Article

Şahin, O., Kaya, G., *, O. Ş. (2025). Boundary value problem for an elastic half plane subjected to distributed moving load. Karaelmas Fen ve Mühendislik Dergisi, Cilt: 15 Sayı: 1, 48–55. https://doi.org/10.7212/karaelmasfen.1518481

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