Çatlak İçeren Bir Çerçeve Taşıyıcı Sistemin Zorlanmış Titreşim Analizi

Year 2020, Volume: 23 Issue: 4, 1059 - 1071, 01.12.2020

Kemal Koçyiğit , Şeref Doğuşcan Akbaş

https://doi.org/10.2339/politeknik.606499

Cited By: 2

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

Supporting Institution

Bursa Teknik Üniversitesi BAP Koordinatörlüğünce

Project Number

172L06

Thanks

Bu çalışma Bursa Teknik Üniversitesi BAP Koordinatörlüğünce desteklenmiştir. Proje Numarası: 172L06.

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

Project Number

172L06

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