Lyapunov Üstelleri Kullanılarak Dönen Bir Bıçağın Titreşimlerinin Stabilite Analizi

Öz

Bu makalede, dönen bir bıçağın titreşim kararlılığının mil titreşim uyarılmasına bağlı olarak analizi sunulmaktadır. Çalışmada kullanılan temel denklem, birden fazla harmonik olarak değişken katsayı terimine sahip Hill tipi doğrusal ikinci dereceden adi diferansiyel denklemdir. Sistemin diferansiyel denklemi, iki birleşmiş birinci mertebeden adi diferansiyel denklem olarak yeniden yazılmıştır. Kararlı ve kararsız bölgeler, rotor hızına, burulma titreşim uyarılma frekansına ve bıçak doğal frekansına ilişkin parametre uzayındaki Lyapunov karakteristik üstelleri tarafından belirlenir. Sonuçlar, genişletilmiş parametreler yöntemiyle (bir pertürbasyon tekniği) elde edilenlerle karşılaştırıldığında, e küçük burulma titreşim genlikleri için mükemmel bir eşleşme gözlemlenmiştir.       

Anahtar Kelimeler

• Kaos,Lineer olmayan dinamik,Lyapunov Üstelleri,Dönen Bıçak Titreşimi,Stabilite

Stability Analysis of Rotating Blade Vibrations Using Lyapunov Exponents

Öz

This paper presents an analysis of the vibration stability of a rotating blade due to shaft torsional vibration excitation. The governing equation adopted in the study is a Hill’s type linear second order ordinary differential equation with multiple harmonically variable coefficient terms. The differential equation of the system is rewritten as two coupled first order ordinary differential equations. The stable and unstable regions are determined by the Lyapunov characteristics exponents on parameter space (grid) relating to the rotor speed, the torsional vibration excitation frequency and the blade natural frequency. The results are contrasted to those obtained by the strained parameter method (a perturbation technique), an excellent match is observed for small torsional vibration amplitudes .

Anahtar Kelimeler

• Chaos,Nonlinear Dynamics,Lyapunov Exponents,Rotating Blade Vibration,Stability

Kaynakça

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