Order-Tuned Vibration Absorbers for a Rotating Flexible Structure with Cyclic Symmetry

This paper investigates the use of order-tuned absorbers to attenuate vibrations of flexible blades in a bladed disk assembly subjected to engine order excitation. The blades are modeled by a cyclic chain of N oscillators, and a single vibration absorber is fitted to each blade. These absorbers exploit the centrifugal field arising from rotation so that they are tuned to a given order of rotation, rather than to a fixed frequency. A standard change of coordinates based on the cyclic symmetry of the system essentially decouples the governing equations of motion, yielding a closed form solution for the steady-state response of the overall system. These results show that optimal reduction of blade vibrations is achieved by tuning the absorbers to the excitation order n, but that the resulting system is highly sensitive to small perturbations. Intentional detuning (meaning that the absorbers are slightly overor under-tuned relative to n) can be implemented in order to improve the robustness of the design. It is shown that by slightly undertuning the absorbers there are no system resonances over the full range of possible rotor speeds, resulting in a system that is robust to mistuning (i.e., small random uncertainties in the system parameters) of the absorbers and/or blades. These results offer a basic understanding of the dynamics of a bladed disk assembly fitted with order-turned vibration absorbers, and serve as a first step to the investigation of more realistic models, where, for example, imperfections, multi-DOF blade models, nonlinear effects, and general-path absorbers are employed.