Forced Vibration Analysis of a Cracked Frame

Abstract

In this study, undamped and damped forced vibration responses of a single span frame with cracks are investigated. The vibration analysis of the cracked frame is examined by using the Euler -Bernoulli beam theory. The local flexibility resulting from the crack effect is modeled with a massless and dimensionless finite element beam in the crack section. The local flexibility is obtained by using the stress intensity factor and strain energy release rates according to the opening mode (Mode 1) and the in-plane shear mode (Mode 2) based on the linear elastic fracture mechanics theory. The crack stiffness is obtained by taking the inverse of the flexibility of the crack. Assembly of global finite element matrices are obtained by adding the crack stiffness to the finite element model.

 

In solution of the forced vibration problem, the central difference method is used in the time history. In the numerical results, the effects of the crack depth, the crack location and dimension of the frame on the undamped and damped forced vibration responses of the cracked frame are investigated. Also, the validation studies are performed in order to accuracy of the presented method.

Keywords

• Crack,frame structure,forced vibration,finite element method

Çatlak İçeren Bir Çerçeve Taşıyıcı Sistemin Zorlanmış Titreşim Analizi

Abstract

Bu çalışmada, kenarında çatlaklar bulunan tek açıklıklı bir çerçeve taşıyıcının sönümsüz ve sönümlü zorlanmış titreşim cevapları incelenmiştir. Çatlaklı çerçevenin titreşim analizleri, Euler-Bernoulli çubuk teorisi çerçevesinde incelenmiştir. Çatlak etkisinden dolayı ortaya çıkan yerel esneklik, çatlak kesiti veya bölgesinde, kütlesiz ve boyutsuz bir çubuk sonlu eleman ile modellenmiştir. Çatlaktan dolayı ortaya çıkan yerel esneklik, lineer elastik kırılma mekaniği teorisi baz alınarak açılma modu (Mod1) ile düzlem içi kayma modu (Mod2) kullanılmasıyla birlikte elde edilen gerilme yığılma faktörü ve şekil değiştirme enerjisi salıverininim oranlarına bağlı olarak elde edilmiştir. Çatlak esnekliğinin tersi alınarak elde edilen çatlak rijitliğinin sonlu elemanlar modeline eklenmesiyle birlikte birleştirilmiş sonlu elemanlar formülasyonları elde edilmiştir.

 

Zorlanmış titreşim çözümlerinde zaman tanım aralığında doğrudan integrasyon yöntemlerinden biri olan merkezi farklar yöntemi kullanılmıştır. Çalışmada farklı değerlerdeki çatlak derinliğinin, farklı çatlak konumunun ve farklı değerlerdeki çerçeve yapının geometrik boyutlarına bağlı olarak dinamik cevaplar elde edilmiş ve yorumlanmıştır. Elde edilen formülasyon ve sonuçların doğruluğu için, literatürdeki benzer çalışmaların özel sonuçları ile kıyaslama çalışmaları yapılmıştır.

Keywords

• Çatlak,Çerçeve Yapı,Zorlanmış Titreşim,Sonlu Elemanlar Metodu

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