Vibration analysis of beams with intermediate supports under moving loads

Yıl 2025, Cilt: 31 Sayı: 5, 744 - 749, 19.10.2025

Emre Gemici , Yaşar Pala

Öz

In this study, transverse vibration of a beam under a moving singular load and a moving moment is investigated. A simply supported beam with intermediate vertical supports modeled according to Euler-Bernoulli beam theory. The intermediate supports are modeled as consisting of a linear spring and a linear damper. The moving force and the moment, the spring force and the damper force are expressed using Dirac delta functions in the equations of motion. Obtaining the exact solution for this problem with classical methods are quite lengthy and complicated. Beam must be divided into spans between each support. Each span must be solved separately with different set of coordinates having same boundary conditions on support points. As the number of support increases, solution becomes more complicated. However, the present method can be used to solve the problem for the whole beam length without having to separate into various spans regardless of number of supports. Dirac delta functions are converted to series expansions which allows us to get exact solution in form of series expansion. This solution than can be easily calculated by a computer. Dynamic responses of several cases such as various number of supports; different support points; various moving load, moving moment and axial load combinations are examined.

Anahtar Kelimeler

Moving load , Moving moment , Simply supported beam , Intermediate supports

Hareketli yüklere maruz ayaklı kirişlerin titreşiminin incelenmesi

Öz

Bu çalışmada, bir kirişin hareketli bir yük ve moment altındaki titreşimi incelenmiştir. Destek ayakları içeren basit mesnetli bir kiriş Euler-Bernoulli kiriş teorisine göre modellenmiştir. Destek ayakları doğrusal bir yay ve doğrusal bir damperden oluştuğu varsayılarak modellenmiştir. Hareketli yük, hareketli moment, yay kuvveti ve damper kuvveti Dirac delta fonksiyonu kullanılarak hareket denklemine dâhil edilmiştir. Klasik yöntemler ile bu problemin kesin çözümünü elde etmek oldukça uzun ve karmaşıktır. Her bir ayak için kiriş, ayaklar arası parçalara bölünerek ele alınmalıdır. Bu parçaların her biri, sınır şartları destek ayak noktalarında olacak şekilde ayrı koordinat eksenlerinde çözümlenmelidir. Ayak sayısı arttıkça çözüm daha da zorlaşacaktır. Mevcut çalışmaya konu yöntemle ayak sayısından bağımsız olarak, kirişi parçalara ayırmadan tüm kiriş boyunca tek bir koordinat ekseninde çözüm elde etmek mümkündür. Dirac delta fonksiyonu seri açılımlarına dönüştürülerek seri açılımı halinde kesin çözüm elde edilmiştir. Çözüm, basit bir bilgisayar programı yazarak hesaplanabilir. Bu çözümle kirişin farklı ayak sayıları; farklı konumlarındaki ayaklar; farklı hareketli yük, hareketli moment ve eksenel yük gibi çeşitli durumlardaki dinamik davranışı incelenmiştir.

Anahtar Kelimeler

Hareketli yük , Hareketli moment , Basit mesnetli kiriş , Destek ayakları

Kaynakça

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