Dynamic stability and nonlinear vibration analysis of a rotor system with flexible/rigid blades

Abstract

In this paper, the primary resonances of a coupled flexible rotor with rigid disk and flexible/rigid blades are investigated. The Euler-Bernoulli beam theory is used to model the blade and shaft. The equations of motion are derived with the aid of the extended Hamilton principle. To simplify the equations of motion, the Coleman and complex transformations are used. The multiple scales method is used to analyze the primary resonances of the system. The influences of mass eccentricity and the damping of the surrounding medium on the steady state responses of the system are studied. It can be seen that rotor's damping values that guarantee the stability of system with flexible blades are higher than those that impose stable conditions in system with rigid blades. In addition, the system with rigid blades becomes completely stable in higher values of the mass eccentricity compared to the system with flexible blades.