| A rigorous formulation of the equations of motion for the vibration of flexible bladed disk-shaft rotor systems both in a rotating frame and in a non-rotating frame is presented for implementation by the finite element method.;A new free-interface component mode synthesis, which uses truncated component real modes, complemented with residual flexibility, inertia-relief modes, and residual dissipative effects, has been developed to analyze the dynamics of damped multi-shaft rotor systems with flexible inter-shaft bearings. All flexible-interface coordinates are eliminated by using the compatibilities of coupling forces on the flexible interfaces.;A general component mode method is then developed as an extension of the above approach, and allows assembly of a damped rotor system with flexible and/or rigid interfaces, using any number of substructures. In this method, all rigid- and flexible-interface coordinates are eliminated from the final set of system equations by utilizing the interface compatibilities.;Many examples compare the accuracy and efficiency of the above methods with other solutions given in the literature.;New eigensolution methods are developed to calculate the critical speeds and whirl speeds for undamped gyroscopic rotor systems, and show that there exists a set of real vectors which constructs a basis for the vector space of the rotor system. A closed-form response is derived, and the characteristics of the response are analytically examined by using the real modes. Based on these methods, a perturbation theory is then developed for lightly damped rotor systems.;Finally, the above methods are applied to the analysis of flexible bladed disk-shaft rotor systems. The effects of bladed disks on the whirl frequencies, critical speeds, steady-state and transient responses of a rotor system are studied. It is concluded that the effects of disc flexibility are only significant for backward whirl modes. For such modes the frequencies can be significantly lowered while the peak responses are increase by the presence of disc flexibility. |
