ÇİFT SİMETRİLİ DEĞİŞKEN KESİTLİ ÇUBUKLARIN EKSENEL TİTREŞİMLERİ

Year 2022, Volume: 8 Issue: 2, 307 - 321, 31.12.2022

Aydın Özmutlu

https://doi.org/10.34186/klujes.1183046

Abstract

Bu çalışmada çift simetrili değişken kesitli çubukların taşıma matrisi yöntemi ile eksenel titreşimleri araştırılmıştır. Ele alınan problemdeki, çubuk açıklık ortasına göre simetrik ve her iki ucundan basit mesnetlidir. Konik çubuk için küresel koordinatlarda yazılan hareket denkleminin degişkenlerine ayırma yöntemi ile Bessel fonksiyonları cinsinden kapalı çözümü yapılmıştır. Simetrik çubuğun 1’inci ve 2’nci bölgesi için çubuk uçlarında durum vektörleri yazılmış ve her iki bölge için taşıma matrisi türetilmiştir. Simetrik çubuk için toplam taşıma matrisi yazılıp sınır koşulları uygulanarak titreşim denklemine ulaşılmıştır. Bu denklemin çözümünden serbest titreşim frekansları ve mod şekilleri farklı koniklik oranları için belirlenmiştir. Koniklik oranın ve simetrinin eksenel titreşim üzerine olan etkisi ortaya konmuştur.

Keywords

Konik çubuk, Eksenel titreşim, Taşıma matrisi, Küresel Bessel fonksiyonları

AXIAL VIBRATIONS OF DOUBLY SYMMETRIC TAPERED BARS

Abstract

In this study, axial vibrations of bi-symmetrical variable cross-section bars were investigated using the transfer matrix method. The bar in the problem under examination is presumptively symmetrical about its mid-span and simply supported at both ends. The doubly symmetric tapered bar's equation of motion, written in spherical coordinates, is solved in closed form employing the separation of variables, and the solution is expressed in terms of Bessel functions. State vectors are obtained at the ends of the symmetrical bar for the first and second domains, and the transfer matrix is computed for both domains. The vibration equation is obtained by writing the total transfer matrix for the symmetrical bar and applying the boundary conditions. From the solution of this equation, free vibration frequencies and mode shapes are determined for different taper ratios. The effect of taper ratio and symmetry on axial vibration has been demonstrated.

Keywords

Tapered bar, Axial vibration, Transfer matrix, Spherical Bessel functions

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