SONLU ELEMAN MODELLEME TEKNİKLERİNİN KİRİŞLERİN DİNAMİK ANALİZİNE ETKİSİ

Kirişlerin serbest ve zorlanmış titreşim davranışlarının analizi, bu yapı elemanlarının tasarım aşamasında incelenmesi gereken en kritik problemlerden biridir. Sınır değer problemlerini çözen sonlu elemanlar yöntemi, titreşim problemlerine de etkin bir şekilde uygulanabilir. Bu çalışmada, iki ucundan sabit mesnetli kirişlerin doğal titreşim frekansları ile sönümlü ve sönümsüz zorlanmış titreşim analizleri incelenmiştir. Analizlerde, iyi bilinen sonlu eleman yazılım paket programları ANSYS ve SAP2000 kullanılmıştır. ANSYS'te Euler-Bernoulli Kiriş teorisine dayanan 2 boyutlu elastik kiriş, Timoshenko kiriş teorisine dayanan 3 boyutlu iki düğümlü ile 3 boyutlu üç düğümlü kiriş elemanları ve dört düğümlü kabuk elemanlar kullanılırken SAP2000'de ise çerçeve elemanı kullanılmıştır. Bu elemanların izotropik kirişin dinamik davranışları üzerindeki etkisi tartışılmıştır. Sonuçlar, serbest ve zorlanmış titreşim için sırasıyla tablo ve grafik şeklinde verilmiştir.

Anahtar Kelimeler:

Serbest Titreşim, Zorlanmış Titreşim, Kiriş, Sonlu Elemanlar Yöntemi, Viskoelastik

EFFECT OF THE FINITE ELEMENT MODELING TECHNIQUES ON THE DYNAMIC ANALYSIS OF BEAMS

Analysis of the free and forced vibration responses of beams is one of the most critical problems to be examined in the design step of these structural members. The finite-element method which solves boundary value problems can be applied efficiently to vibration problems. In this study, the natural vibration frequency and damped and undamped transient analyses of the pinned-pinned beams are investigated. The well-known finite-element software packages, ANSYS and SAP2000, are used. The 2-D elastic beam which is based on the Euler-Bernoulli Beam theory, 3-D two-node and 3-D three-node beam elements which are based on Timoshenko beam theory, and four-node shell elements are used in ANSYS and the frame member is utilized in SAP2000. The effect of these elements on the dynamic behaviors of the isotropic beam is discussed. The results are given in tabular and graphical form for the free and forced vibration, respectively.

Keywords:

Free Vibration, Forced Vibration, Beam, Finite-Element Method, Viscoelastic,

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