KALIN CİDARLI İÇİ BOŞ SİLİNDİRLERİN DOĞAL FREKANSLARININ DIŞ/İÇ ÇAP ORANI VE SINIR ŞARTLARI İLE DEĞİŞİMİ
Bu çalışmada, sonsuz uzunlukta, kalın cidarlı, homojen ve izotrop lineer elastik malzemeden yapılmış içi boş silindirlerin serbest titreşim analizi analitik olarak çalışılmıştır. Öncelikle elastisitenin alan denklemleri kullanılarak, Lame sabitleri cinsinden hareket denklemi elde edilmiş, daha sonra bu denklem Bessel fonksiyonları yardımıyla kapalı olarak çözülmüştür. Her bir olası klasik sınır şartı için, karakteristik serbest titreşim denklemi kapalı formda sunulmuştur. Şimdiki çalışmadan elde edilen sonuçların mevcut literatürle doğrulanması sonrası parametrik bir çalışma gerçekleştirilmiştir. Boyutsuz serbest titreşim frekanslarının sınır şartları ve silindir dış çap/iç çap oranı ile değişimleri grafik olarak gösterilmiş, sonuçların bazıları da tablo halinde sunulmuştur
Anahtar Kelimeler:
Serbest Titreşim, Doğal Frekans, Silindirik, Bessel Fonksiyonu, Analitik Çözüm
In this study exact free vibration analysis is performed for thick-walled infinite hollow cylinders made of an isotropic and homogeneous linear elastic material. Equation of motion in terms of Lame constants is first derived from field equations of elasticity, and then solved analytically with the help of Bessel’s functions. For each classical possible boundary condition the characteristic free vibration equation is presented in closed forms. After verifying the present results with the available literature a parametric study is conducted. Variation of the dimensionless natural frequencies with respect to the boundary conditions and the cylinder aspect ratio outer radius/inner radius is illustrated graphically and some numerical results are given in tabular form
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- Başlangıç: 2015
- Yayıncı: İstanbul Teknik Üniversitesi