VIBRATION ANALYSIS OF ROTATING TIMOSHENKO BEAMS WITH DIFFERENT MATERIAL DISTRIBUTION PROPERTIES

Öz

In this study, vibration characteristics of functionally graded rotating Timoshenko beams that undergoes flapwise bending vibration are analysed. Beam models with different material distribution properties are considered. The energy expressions are derived by introducing several explanotary figures and tables. Applying the Hamilton’s Principle to the derived energy expressions, governing differential equations of motion and the boundary conditions are obtained. Related formulation is coded by using MATLAB and in the solution part, the equations of motion, including the parameters for the rotary inertia, shear deformation, power law index parameter and slenderness ratio are solved using an efficient mathematical technique, called the differential transform method (DTM).   Natural frequencies of the modeled beams are obtained. Increasing effects of the slenderness ratio and the rotational speed and the decreasing effect of the power-law index on the natural frequencies are investigated. Moreover, differences between the natural frequencies of the beam models with different material distribution characteristics is noticed and examined.  Obtained results are distributed in several tables.

Anahtar Kelimeler

• Differential Transform Method,Functionally Graded Beam,Rotating Timoshenko Beam

Fonksiyonel Derecelendirilmiş Dönen Timoshenko Kirişlerin Titreşim Analizi

Öz

Bu çalışma kapsamında, düzlem dışı eğilme (flaplama hareketi) deplasmanı altında fonksiyonel derecelendirilmiş, dönen Timoshenko kirişlerin titreşim analizi yapılmıştır. Farklı malzeme dağılımlarına sahip kiriş modelleri incelenmiş ve enerji ifadeleri, çeşitli şekil ve tablolar kullanılarak çıkarılmış ve bu enerji denklemlerine Hamilton Prensibi uygulanarak hareket denklemleri ve sınır şartları elde edilmiştir ve ilgili denklemler, MATLAB programında kodlanmıştır. Çözüm aşamasında; dönme ataleti, kayma etkisi, malzeme dağılımı üstel fonksiyonu, kiriş narinlik oranı gibi çok çeşitli parametrelerin katıldığı hareket denklemleri ve sınır şartlarına, etkin ve hızlı bir matematiksel yöntem olan Diferansiyel Dönüşüm Yöntemi (Differential Transform Method) uygulanmıştır. Modellenen kirişlere ait doğal frekanslar hesaplanmıştır. Narinlik oranı ve dönme hızının frekanslar üzerindeki yükseltici etkileri ve malzeme dağılımı ile ilgili olarak güç indeksinin, frekanslar üzerindeki azaltıcı etkisi incelenmiştir. Ayrıca, farklı malzeme dağılım karakterlerine sahip kirişlere air frekans değerleri arasındaki farklar fark edilmiş ve incelenmiştir. Elde edilen sonuçlar, çeşitli tablolarda sunulmuştur.

Anahtar Kelimeler

• Diferansiyel Dönüşüm Yöntemi,Dönen Timoshenko Kiriş,Fonksiyonel Derecelendirilmiş Kiriş

Kaynakça

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