Stability Analysis of Rotating Blade Vibrations Using Lyapunov Exponents
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Date
2018
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Abstract
This paper presents an analysis of the vibration stability of a rotating blade due to shaft torsionalvibration excitation. The governing equation adopted in the study is a Hill’s type linear second order ordinarydifferential equation with multiple harmonically variable coefficient terms. The differential equation of thesystem is rewritten as two coupled first order ordinary differential equations. The stable and unstable regions aredetermined by the Lyapunov characteristics exponents on parameter space (grid) relating to the rotor speed, thetorsional vibration excitation frequency and the blade natural frequency. The results are contrasted to thoseobtained by the strained parameter method (a perturbation technique), an excellent match is observed for smalltorsional vibration amplitudes .