Lyapunov Üstelleri Kullanılarak Dönen Bir Bıçağın Titreşimlerinin Stabilite Analizi

Authors : Tarık Kunduraci

Pages : 11-23

Doi:10.31202/ecjse.339035

View : 11 | Download : 7

Publication Date : 2018-01-31

Article Type : Research

Abstract :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 .
Keywords : Chaos, Nonlinear Dynamics, Lyapunov Exponents, Rotating Blade Vibration, Stability