Analytical methods of nonsynchronous response and bifurcation in nonlinear rotordynamics with applications

A thorough study of analytical methods for nonsynchronous responses and bifurcation in nonlinear rotordynamics is carried out. Various relevant applications are discussed. Novel and powerful methods for analyzing quasi-periodic response and the corresponding stability are developed. Applications of these methods to complicated rotor-bearing systems are explored by means of numerical computer modeling.; The existence of nonlinear mechanisms that explain nonsynchronous responses of turbomachinery rotor system is discussed. Limitations of linearization methods, that are extensively applied as traditional analysis methods, are enumerated. A general analysis procedure for nonlinear rotordynamics is developed. Finite element method and modal reduction techniques are introduced into the nonlinear analysis. Various nonlinear steady state responses including nonsynchronous periodic response and quasi-periodic response are discussed. Stability of each type of solution and bifurcations following the loss of stability are also studied.; A Fixed Point Algorithm (FPA) for locating periodic solutions is discussed in detail. The Floquet theory is utilized for predicting the stability of periodic solutions. An FPA for quasi-periodic solutions is constructed through an interpolation procedure on a second order Poincare map. A new method called Farey Tree Bisection Method is developed for asymptotically approaching the winding number of a quasi-periodic torus. For stability analysis of a quasi-periodic solution, a "Comb-Searching Method" based on extended Floquet theory is first used. The new method is a simultaneous search that starts from a set of uniformly distributed initial points in the state space. The Floquet multipliers and exponents are found from a resultant quasi-monodromy matrix.; As examples, two rotor systems, one with Floating Ring Bearings and the other with Auxiliary Bearings, are analyzed. Phenomena of nonsynchronous responses and types of bifurcation are rich and varied in these applications.