Karma mesnetli kirişlerin titreşim analizi
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Date
2019-09-04
Authors
Beyçimen, Semih
Journal Title
Journal ISSN
Volume Title
Publisher
Bursa Uludağ Üniversitesi
Abstract
Bu tezde farklı sınır şartları altında bulunan kirişlerin serbest ve sönümleyici titreşimleri incelenmiştir. Genel bir çözüm vermesi açısından karmaşık bir kiriş modeli oluşturulmuş ve bu model hem Euler-Bernoulli hem de Timoshenko kiriş teorileri ile incelenmiştir. Matlab programı yardımı ile sayısal olarak bulunan değerler çeşitli parametrelere göre kıyaslanıp yorumlanmıştır. Ayrıca kademeli veya çatlak bulunan kirişlerin titreşim analizleri de genel bir kiriş modeli üzerinde incelenmiştir. Böylece birçok durumu kapsayan geniş bir model oluşturulmuştur. Çalışmada her iki kiriş teorisi ile incelenen çatlaklı kirişlerin sayısal sonuçları arasında farkın büyük olduğu ve deneysel çalışmalar ile kıyaslandığında Timoshenko kiriş teorisinin Euler-Bernoulli giriş teorisine göre daha doğru sonuçlar verdiği gözlemlenmiştir. Çalışmada çatlak, hem dönme yayı hem de dönme ve ötelenme yayı olarak düşünülmüş ve bu iki model arasında kıyaslama yapılmıştır. Bu inceleme sonucunda sadece dönme yayı olarak kullanılan modelin Euler-Bernoulli kirişler için uygun olduğu fakat Timoshenko kirişler için uygun olmadığı ve Timoshenko kirişlerde hem dönme hem de ötelenme yayı olarak kurulan çatlak modelinin daha uygun olduğu sonucuna varılmıştır. Bunun nedeni Timoshenko kirişte, dönme ve ötelenme yayı olarak modellenen çatlağın çatlak bölgesinde kesme kuvvetlerini iletmesidir.
In this thesis, free and damping vibrations of beams under different boundary conditions have been investigated. In order to provide a general solution, a complex beam model has been created and this model has been examined with both Euler-Bernoulli and Timoshenko beam theories. By the Matlab program, numerical values have been compared with respect to various parameters. Besides, vibration analysis of stepped or cracked beams have been examined by using a general beam model. Thus, a wide model has been created covering many situations. In the study, it has been observed that there is a big difference between the numerical results of the cracked beams examined with both beam theory and Timoshenko beam theory gives more accurate results than Euler-Bernoulli beam theory with respect to experimental studies. In this study, the crack is considered as both the spring of rotation and the spring of rotation and translational and comparison is made between these two models. As a result of this investigation, it has been concluded that the cracked model used only as a rotation spring has been suitable for Euler-Bernoulli beams but not for Timoshenko beams and the crack model established as both rotation and translational spring in Timoshenko beams has been more appropriate. Because Timoshenko beam transmits shear forces in zone of the crack modeled as a spring of rotation and translational.
In this thesis, free and damping vibrations of beams under different boundary conditions have been investigated. In order to provide a general solution, a complex beam model has been created and this model has been examined with both Euler-Bernoulli and Timoshenko beam theories. By the Matlab program, numerical values have been compared with respect to various parameters. Besides, vibration analysis of stepped or cracked beams have been examined by using a general beam model. Thus, a wide model has been created covering many situations. In the study, it has been observed that there is a big difference between the numerical results of the cracked beams examined with both beam theory and Timoshenko beam theory gives more accurate results than Euler-Bernoulli beam theory with respect to experimental studies. In this study, the crack is considered as both the spring of rotation and the spring of rotation and translational and comparison is made between these two models. As a result of this investigation, it has been concluded that the cracked model used only as a rotation spring has been suitable for Euler-Bernoulli beams but not for Timoshenko beams and the crack model established as both rotation and translational spring in Timoshenko beams has been more appropriate. Because Timoshenko beam transmits shear forces in zone of the crack modeled as a spring of rotation and translational.
Description
Keywords
Çatlak, Beam, Doğal frekans, Kademe, Kiriş, Mod şekli, Titreşim, Crack, Mode shape, Natural frequency, Stepped, Vibration
Citation
Beyçimen, S. (2019). Karma mesnetli kirişlerin titreşim analizi. Yayınlanmamış yüksek lisans tezi. Bursa Uludağ Üniversitesi Fen Bilimleri Enstitüsü.