Farklı geometrik boşluklu eğri eksenli petek kirişlerin sonlu elemanlar yöntemi ile serbest titreşim analizi

Gövdesinde boşluk bulunan eğri eksenli petek kirişler, daha az çelik malzeme ile daha yüksek mukavemet sağlamaları, dolayısı ile tasarımcıya daha ekonomik bir çözüm yolu sunmaları bakımından tercih edilmektedir. Günümüzde havaalanları, stadyumlar vb. yapı türlerinde sıklıkla rastlayabileceğimiz eğri eksenli petek kirişlerde, farklı geometrik şekillerde boşluk tipleri kullanılabilmektedir. Yapılan çalışmada, gövdesinde farklı geometrik boşluklar bulunan eğri eksenli petek kirişlerin düzlem içi serbest titreşimi üç boyutlu sonlu elemanlar yöntemi kullanılarak incelenmiştir. Gövde boşluk geometrisinin petek kirişlerin serbest titreşim analizi yardımı ile genlik ve frekans değerlerine etkisi detaylı bir şekilde araştırılmıştır. Bu amaçla yapılan modal analizlerde, daire, kare, beşgen ve altıgen olmak üzere 4 farklı türde gövde boşluk tipi dikkate alınmıştır Modellemelerde IPE220, IPE240 ve IPE300 profilleri tercih edilmiş olup 10 düğümlü tetrahedral tipi sonlu eleman modeli kullanılarak analizler gerçekleştirilmiştir. Çalışmada kullanılan malzeme, lineer homojen izotropik bir malzeme olup, çeliğin mekaniksel özellikleri dikkate alınmıştır. Çalışma kapsamında ele alınan profillerin uç mesnetlenme koşulları, ankastre - ankastre, ankastre - sabit ve ankastre - serbest olarak planlanmış ve söz konusu profillerin her biri bu üç sınır koşulu dikkate alınarak serbest titreşim analizine tabi tutulmuştur. Analizlerden elde edilen sonuçlar IPE220, IPE240 ve IPE300 profillerinden oluşan daire, kare, beşgen ve altıgen boşluklu eğri eksenli petek kirişler için detaylı bir şekilde sunulmuştur. Yapılan tahkikler gövde boşluk tipinin, boşluklu eğri eksenli petek kirişlerin serbest titreşim davranışı üzerinde önemli ölçüde etkili olduğunu göstermektedir.

Anahtar Kelimeler:

Doğal titreşim frekansları, Eğri eksenli kirişler, Petek kiriş, Serbest titreşim analizi, Sonlu elemanlar yöntemi

Free vibration analysis of curved castellated beams with different geometric web openings by the finite element method

Curved castellated beams with web openings are preferred because they provide higher strength with less steel material, and therefore offer a more economical solution to the designer. Different geometric shapes of the web opening types can be used in the curved castellated beams which can often be seen in airports, stadiums, etc nowadays. This study investigates the in-plane free vibration behavior of curved castellated beams with different geometric web openings using the three-dimensional finite element method. The effect of the web-opening geometrical shapes on the amplitude and natural frequency values of the curved castellated beams is investigated in detail via free vibration analysis. In the modal analysis done for this purpose, 4 different types of web opening types circle, square, pentagon and hexagon are taken into consideration. IPE 220, IPE 240, and IPE300 profiles are preferred in the modeling, and analysis are carried out using a 10-node tetrahedral finite element model. The material used in this study is a linear homogeneous isotropic material, and the mechanical properties of the steel are considered. The end support conditions of the profiles considered within the scope of the study are planned as fixed - fixed, fixed - pinned, and fixed - free supported. Each of the aforementioned profiles is subjected to free vibration analysis considering these three boundary conditions. The results obtained from the analysis are presented in detail for curved castellated beams with circular, square, pentagonal, and hexagonal web openings consisting of IPE 220, IPE 240, and IPE300 profiles. The investigations show that the web opening type has a significant effect on the free vibration behavior of curved castellated beams.

Keywords:

Natural frequency, Curved beams, Castellated beams, Free vibration analysis, Finite element method,

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