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.
In this study, the freedom of vibration characteristics of the correct axis functionally scaled (FD) material curves based on the theory of the first staircase sliding deformation were studied. It is accepted that the characteristics of the material only changed throughout the thickness of the curve. The effects of the material exchange rate, the length/thickness ratio and the limit conditions on the freedom of vibration behavior of the curves have also been studied parametrically. The movement equations that manage the freedom of vibration behavior of these curls were obtained using the minimum total energy principle based on the Timoshenko curl assumption. These addifferential equations obtained in a canonical way are resolved numerically by the Complementary Functions Method (TFY). The calculated natural vibration frequencies have been compared with the results of existing studies in literature and have been shown to be in harmony with them.
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.
Alan : Mühendislik
Dergi Türü : Ulusal
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