Stability Analysis of Rotating Blade Vibrations Using Lyapunov Exponents

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 .