Timuçin Alp ASLAN, Ahmad Reshad NOORI, Beytullah TEMEL

Birinci Mertebe Kayma Deformasyon Teorisine Dayalı FD Düz Eksenli Kirişlerin Serbest Titreşim Analizi

Bu çalışmada, birinci mertebe kayma deformasyon teorisine dayalı doğru eksenli fonksiyonel derecelenmiş (FD) malzemeli kirişlerin serbest titreşim özellikleri incelenmiştir. Malzeme özelliklerinin sadece kiriş kalınlığı boyunca değiştiği kabulü yapılmıştır. Malzeme değişim katsayısının, uzunluk/kalınlık oranlarının ve sınır koşullarının kirişlerin serbest titreşim davranışı üzerindeki etkileri de parametrik olarak incelenmiştir. Bu kirişlerin serbest titreşim davranışını idare eden hareket denklemleri, Timoshenko kiriş varsayımına dayalı minimum toplam enerji ilkesi kullanılarak elde edilmiştir. Kanonik halde elde edilen bu adi diferansiyel denklemler Tamamlayıcı Fonksiyonlar Yöntemi (TFY) ile sayısal olarak çözülmüştür. Hesaplanan doğal titreşim frekansları, literatürdeki mevcut çalışmaların sonuçları ile karşılaştırılmış ve bunlarla uyum içerisinde olduğu gösterilmiştir.

Free Vibration Analysis of FG Straight-Axis Beams Based on the First-Order Shear Deformation Theory

In this work, the free vibration characteristics of functionally graded (FG) beams with straight-axis are investigated based on the first-order shear deformation theory (FSDT). It is assumed that the material properties change only through the thickness of the beam. The effects of the coefficient of variation, length/thickness ratios and boundary conditions on the free vibration behavior of the beams are also examined in a parametric manner. The equations of motion, governing the free vibration behavior of these beams are obtained using the principle of minimum total energy based on the Timoshenko’s beam assumption. These ordinary differential equations (ODEs) obtained in the canonical form are solved numerically by the Complementary Functions Method (CFM). The calculated natural vibration frequencies are compared with the results of the existing studies in the literature and shown to be in agreement with them.

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