Fonksiyonel Derecelenmiş Malzeme ve Değişken Kesitli Silindirik Olmayan Helisel Çubukların Titreşimi

Bu çalışmada fonksiyonel derecelenmiş malzemeli değişken kesite sahip silindirik olmayan helisel çubukların serbest titreşimi incelenmiştir. Malzeme ve kesit değişiminin çubuk ekseni boyunca olduğu varsayımı kullanılmıştır. Eksenel ve kayma deformasyonlarını içeren çubuğun serbest titreşimini idare eden diferansiyel denklemler Timoshenko kiriş teorisi kullanılarak elde edilmiştir. Ardından taşıma matrisi ve rijitlik matrisi yöntemleri bir arada kullanılarak diferansiyel denklemler sayısal olarak çözülmüştür. Malzeme değişim parametresi (βmat), kesit değişim parametresi (βsec) silindirin kenar ve orta kısımlarının yarıçap oranının R2⁄R1 hiperbol ve varil tipi geometriye sahip silindirik olmayan helisel çubukların serbest titreşimine etkisi araştırılmıştır. Literatürde bulunan örnek ve ANSYS paket programı kullanılarak elde edilen sonuçlar karşılaştırılmalı olarak verilmiştir.

Anahtar Kelimeler:

Fonksiyonel derecelenmiş malzeme, Serbest titreşim, Silindirik olmayan helisel çubuk, Değişken kesit

Vibration Analysis of Non-Cylindrical Helical Rods with Functionally Graded Materials and Variable Cross-sectional Area

In this study, free vibration of non-cylindrical helical rods of variable cross-section with functionallygraded material was investigated. Material and cross-section variation are assumed to be along the rodaxis. The differential equations governing the free vibration of the rod including axial and shear deformations are obtained by using the Timoshenko’s beam theory. Then, the obtained differential equations are solved numerically by using the transfer matrix and stiffness matrix methods simultaneously. The effect of material variation parameter (βmat), cross section variation parameter (βsec), ratio of the edge and middle point radiuses of the cylinder (R2⁄R1) on the free vibration behaviour of hyperboloidal and barrel type non-cylindrical helical rods were investigated. The results obtained from the present study are compared with the example available in the literature and the ANSYS package program.

Keywords:

Functionally graded material, Free vibration, Non-cylindrical helical rod, Variable crosssection,

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