Transient response of flexible rotor with arbitrarily distributed mass through critical speed

In this paper, the Riccati transfer matrix method and the component theory of forward and backward whirls are used to the eigenproblem of damped free whirling vibration of a flexible rotor with arbitrarily distributed mass on isotropic or anisotropic supports, with the gyroscopic effect taken into account to find out its critical speeds and corresponding vibrational shape functions. The generalized damped mode theory is developed and extended, which is employed in combination with the Bogoliubov-Mitropolskii asymptotic method to deduce two sets of first order differential equations to calculate the transient response of the rotor with limited power supply passing through its critical speeds in forward whirl and backward whirl respectively. The coupling phenomenon of the rotor through two neighboring critical speeds is also analyzed.