VIBRATION ANALYSIS OF ROTATING TIMOSHENKO BEAMS WITH DIFFERENT MATERIAL DISTRIBUTION PROPERTIES

Year 2019, Volume: 7 Issue: 2, 272 - 286, 01.06.2019

Özge Özdemir

https://doi.org/10.15317/Scitech.2019.198

Abstract

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.

Keywords

Differential Transform Method, Functionally Graded Beam, Rotating Timoshenko Beam

Fonksiyonel Derecelendirilmiş Dönen Timoshenko Kirişlerin Titreşim Analizi

Abstract

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.

Keywords

Diferansiyel Dönüşüm Yöntemi, Dönen Timoshenko Kiriş, Fonksiyonel Derecelendirilmiş Kiriş

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