Application of the Differential Transform Method in Static Analysis of Ballasted Railway Tracks

Öz

Many problems in engineering are simplified under certain assumptions and a mathematical model of the simplified model is created and the solution is reached using analytical or numerical methods. One of these simplified models is the theory of beams resting on elastic foundations. Beam theory resting on elastic foundation is an approach used in the solution of railway track and gives suitable results. The simplest approach used in modeling problems of beams resting on elastic foundations is the Winkler soil model, which represents the effect of the soil on the beam with a single parameter. In this study, the differential transformation method approach is proposed for the static analysis of ballasted railway track. In the study, the ballasted railway track was modeled as an Euler-Bernoulli beam resting on the Winkler foundation, known from the literature. First, the differential equation and boundary conditions of the beam resting on the equivalent Winkler foundation were written, and then the differential equation and boundary conditions were made dimensionless to facilitate the solution. The solution of the dimensionless fourth-order ordinary differential equation was carried out by the differential transformation method, considering the boundary conditions. At the end of the study, an example taken from the literature was solved to investigate the suitability of the solution with the differential transformation method and the results were evaluated.

Anahtar Kelimeler

• Ballasted railway track
• Winkler soil model
• Differential transform method
• Static analysis

Balastlı Demiryolu Hatlarının Statik Analizinde Diferansiyel Dönüşüm Yönteminin Uygulanması

Öz

Mühendislikte birçok problem belirli kabuller altında basitleştirilmekte ve basitleştirilmiş modelin matematik modeli kurularak analitik ya da sayısal yöntemler ile çözüme ulaşılmaktadır. Bu basitleştirilmiş modellerden birisi de elastik zemine oturan kiriş teorisidir. Elastik zemine oturan kiriş teorisi demiryolu hatlarının çözümünde kullanılan ve uygun sonuçlar veren bir yaklaşımdır. Elastik zemine oturan kiriş problemlerinin modellenmesinde kullanılan en basit yaklaşım ise zeminin kirişe etkisini tek bir parametre ile temsil eden Winkler zemin modelidir. Bu çalışmada balastlı demiryolu hatlarının statik analizi için diferansiyel dönüşüm yöntemi yaklaşımı önerilmiştir. Çalışmada balastlı demiryolu hattı literatürden bilinen Winkler zeminine oturan bir Euler-Bernoulli kirişi olarak modellenmiştir. Önce eşdeğer Winkler zeminine oturan kirişin diferansiyel denklemi ve sınır koşulları yazılmış daha sonra çözümü kolaylaştırmak için diferansiyel denklem ve sınır koşulları boyutsuz hale getirilmiştir. Boyutsuz dördüncü mertebeden adi diferansiyel denklemin çözümü sınır koşulları dikkate alınarak diferansiyel dönüşüm yöntemi ile gerçekleştirilmiştir. Çalışmanın sonunda diferansiyel dönüşüm yöntemi ile çözümün uygunluğunu araştırmak üzere literatürden alınan bir örnek çözülmüş ve sonuçlar değerlendirilmiştir.

Anahtar Kelimeler

• Balastlı demiryolu hattı
• Winkler zemin modeli
• Diferansiyel dönüşüm yöntemi
• Statik analiz

Kaynakça

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