Eksenel fonksiyonel derecelendirilmiş helislerin karışık sonlu eleman yöntemi ile serbest titreşim analizi

Öz

Bu çalışmanın amacı, eksenel fonksiyonel derecelendirilmiş (EFD) kesin geometri tarifi üzerinden elde edilen dairesel olmayan (fıçı, hiperboloidal ve eliptik) helislerin doğal frekanslarını incelemektir. Timoshenko çubuk kuramı üstünden geliştirilen karışık sonlu eleman yönteminde kesit çarpılması da gözetilerek serbest titreşim analizi yapılmıştır. İki düğüm noktalı eğrisel sonlu elemanın her düğüm noktasındaki 12 değişken; üçü yer değiştirmeler, üçü kesit dönmeleri, üçü kuvvetler ikisi eğilme biri burulma momentleridir. Eksenel FD dairesel olmayan geometriye sahip ve kesin geometri üzerinden tariflenen helislerin serbest titreşim analizi farklı sınır koşulları ve malzeme gradyenti değişimleri üzerinden detaylıca tartışılmıştır. Yöntem literatür ya da ANSYS ile doğrulandıktan sonra literatür için tamamen özgün problemler çözülmüştür

Anahtar Kelimeler

• kesin helis geometrisi
• Foksiyonel derecelendirilmiş malzeme
• Sonlu eleman
• Çarpılma
• Serbest titreşim analizi

Free vibration analysis of axially functionally graded helices via mixed finite element method

Abstract

The objective of this study is to investigate the natural frequencies of axially functionally graded (AFG) non-circular (barrel, hyperboloidal and elliptical) helices based on exact geometry. Free vibration analysis is performed using the mixed finite element method based on Timoshenko beam theory by considering cross-sectional warping effect. A two-noded curved finite element involves 12 field variables at each node, three displacements, three cross-sectional rotations, three forces, and three moments. The free vibration analysis of axially FG exact non-circular helical geometries is discussed in detail over different boundary conditions and material gradient indexes. After verifying the algorithm with the problems available in the literature and ANSYS software, original problems for the literature are solved.

Keywords

• Exact helix geometry
• Functionally graded material
• Finite element
• Warping
• Free vibration analysis

Kaynakça

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