A fuzzy approach for the analysis of unbalanced nonlinear rotor systems

The components of most structural and mechanical systems exhibit considerable variations or uncertainties in their properties. Thus, the performance characteristics of such systems are also subject to uncertainties. In the case of a rotor-bearing system, the nonlinear bearing restoring force is usually represented as a third or fourth power of displacement or as a piecewise linear function of displacement. The coefficients of these models are acquired from experiments and approximations, and will vary considerably during the operation of the bearing. Hence, it is more reasonable to treat them as uncertain values. Other bearing parameters such as the inertial properties of concentrated disks, distributed mass and damping of the rotating assemblies are also uncertain due to manufacturing and assembly errors and imprecise operating conditions. It is known that the vibration response of a rotor is highly sensitive to small fluctuations or variations in the bearing parameters. Therefore, any realistic analysis and design of rotor-bearing systems must take the uncertainties into account. In this paper, a methodology is presented for the fuzzy analysis of nonlinear rotor-bearing systems along with numerical results to demonstrate the computational feasibility of the methodology.