Öz

In this paper, periodic structure theory with the wave approximation is used to present a simple approximate solution technique to characterize wave motions propagating in periodic line-supported cylinders in the circumferential direction. To develop displacement functions that adhere to Floquet's concept, a combination of simple beam functions of the bounding modes(BM)of propagation bands(PB) of a periodic beam are formulated. This study is developed for the motion type known as a plane wave. Consequently, only waves that are simply propagating without attenuation are taken into account. The circumferential modes of a single periodic curved panel (unit cell) have been defined in terms of classical beam functions that satisfy Floquet's wave principle, but the axial modes are thought to be sinusoidal waves. Displacement functions are used to strain energy and kinetic energy expressions. The RayleighRitz technique is then used to generate the stiffness and mass matrices of the periodic unit cell. By solving the eigenvalue equation, phasefrequency relation is obtained. It has also been possible to predict the bounding frequencies of the PB for various axial modes of a cylindrical shell with a certain circumferential phase constant. The findings are then put through comparison with those outlined in the literature. Further, the bounding frequency results for the optimum periodic curved panel which gives lowest frequency for a given cylindrical shell geometry are also found out. It has been found that the current beam function with a periodic structure (PS) wave approach can find the bounding frequencies (BF) and bounding modes (BM) with reasonable accuracy.

Anahtar Kelimeler

• Cylindrical shell
• Curved panel
• Wave propagation
• Bounding frequency
• Beam function
• Rayleigh-Ritz method

Determination of bounding frequencies of cylindrical shells using a periodic structure wave approach with Rayleigh-Ritz method

Öz

Bu çalışmada, dalga yaklaşımı ile periyodik yapı teorisi, çevresel yönde periyodik çizgi destekli silindirlerde yayılan dalga hareketlerini karakterize etmek için basit bir yaklaşım çözüm tekniği sunmak için kullanılmaktadır. Floquet'nin kavramına uygun yer değiştirme fonksiyonları geliştirmek için, periyodik bir kirişin yayılma bantlarının (PB) sınırlar modlarının (BM) basit kiriş fonksiyonlarının bir kombinasyonu formüle edilmiştir. Bu çalışma düzlem dalga olarak bilinen hareket türü için geliştirilmiştir. Sonuç olarak, yalnızca zayıflama olmaksızın yayılan dalgalar dikkate alınmıştır.Tek bir periyodik eğri panelin (birim hücre) çepeçevrgi modları, Floquet'in dalga prensibini karşılayan klasik ışın fonksiyonları açısından tanımlanmıştır, ancak eksenel modların sinüzoidal dalgalar olduğu düşünülmektedir.Yer değiştirme fonksiyonları, gerinim enerjisi ve kinetik enerji ifadelerini germek için kullanılır. Rayleigh-Ritz tekniği daha sonra periyodik birim hücrenin sertlik ve kütle matrislerini oluşturmak için kullanılır. Özdeğer denkleminin çözülmesiyle fazfrekans ilişkisi elde edilir. Belirli bir çepeçevrgi faz sabiti ile silindirik bir kabuğun çeşitli eksenel modları için PB'nin sınırlar frekanslarını tahmin etmek de mümkün olmuştur. Elde edilen bulgular daha sonra literatürde belirtilenlerle karşılaştırılmıştır. Ayrıca, belirli bir silindirik kabuk geometrisi için en düşük frekansı veren optimum periyodik kavisli panel için sınırlar frekansı sonuçları da bulunmuştur. Periyodik yapı (PS) dalga yaklaşımına sahip mevcut ışın fonksiyonunun sınırlar frekansları (BF) ve sınırlar modları (BM) makul bir doğrulukla bulabildiği tespit edilmiştir

Anahtar Kelimeler

• Silindirik kabuk
• Kavisli panel
• Dalga yayılımı
• Sınırlama frekansı
• Işın işlevi
• Rayleigh-Ritz yöntemi

Kaynakça

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