Localization in nonlinear mistimed systems with cyclic symmetry

In forced systems with cyclic symmetry localization can occur due to parameter uncertainties. Often, Monte-Carlo simulations are used to find regions, where the system response is sensitive to parameter uncertainties. These simulations require a large computation time. Therefore, an approximate method to calculate the envelopes of the frequency response functions is developed in this paper. An example of a nonlinear system with cyclic symmetry is a bladed disk assembly with friction dampers. Friction dampers can be installed underneath the blade platforms of turbine blades. Due to dry friction and the relative motion between blades and dampers, energy is dissipated, which results in a reduction of blade vibration amplitudes. By optimizing the mass of the friction dampers, the best damping effects are obtained, which lead to an increase in the reliability of the turbine. In this paper, the calculated response of a mistimed bladed disk assembly with friction dampers is discussed. An approximate method is developed to calculate the envelopes of the corresponding frequency response function for statistically varying eigenfrequencies of the blades. Regions where localization can occur with a high probability, are calculated by this method.