The goal of this work is to investigate the performance of order-tuned absorbers for vibration reduction in cyclic and nearly cyclic systems. The applications of interest are structural systems such as turbine blades, bladed disk assemblies, blisks (integral disk-blade systems), and helicopter rotor blades. These flexible structures rotate at a constant speed and are subjected to traveling wave dynamic loading, resulting in component vibrations that can cause high cycle fatigue failure, noise, reduced performance, and other undesirable effects. A natural means of reducing these vibrations and their attendant problems is the implementation of tuned vibration absorbers. Centrifugally-driven, order-tuned vibration absorbers are ideally suited for this task, yet this approach has received scant attention to date.
This project will consider a systematic study of the performance of order-tuned vibration absorbers in individual rotating flexible components and in cyclic systems of interconnected substructures. The basic design features of these absorbers will be explored by considering a hierarchy of models for rotating structural elements fitted with absorbers. The models for the structural members will range from single-degree-of-freedom oscillators to industry-based finite element models. The features of the absorber models will be focused on design-related parameters, specifically: the placement of the absorber on the primary structure, the absorber mass ratio relative to that of the primary structure, the path along which the absorber travels (which sets its linear and nonlinear tuning parameters), and the effects of impacts when the absorber reaches its rattle space limitations. The response of these systems will be analyzed by exploiting the symmetry of the system and will utilize a range of tools that includes linear vibration analysis for cyclic systems, perturbation and bifurcation techniques for symmetric nonlinear systems, matching methods for impacting motions, hybrid time-frequency domain techniques, and simulations of equations of motion. The effects of unavoidable imperfections that destroy the perfect cyclic symmetry (such as blade mistuning) will also be considered. It is known that certain patterns of mistuning among subsystems can drastically reduce worst-case forced response levels, and we will examine the effectiveness of using absorbers tuned to different orders to achieve these effects. In this case the absorbers will serve a dual purpose: to attenuate vibrations in the blade to which they are attached, as well as to provide a pattern of system detuning that reduces vibrations in the overall structure. The general aim of these analyses will be to provide predictive tools that can be used to help select absorber parameters for optimal performance.
The proposed research will impact the fundamental understanding of the performance of vibration absorbers, as described above, and will also involve education, outreach, and technology transfer. In terms of education, the PIs will include the linear vibration analyses of these systems in standard vibration courses at both the undergraduate and graduate levels, and some of the nonlinear aspects of the systems will be used as motivating examples and exercises for graduate courses in nonlinear vibrations. In addition, the Michigan State University PIs are involved in a summer outreach program that exposes high school students to the mechanical engineering profession. One topic presented to the students is the practical use of vibration absorbers, and their application to systems such as turbine blades in jet engines will be a natural fit into that program. In the area of technology transfer, the University of Michigan PIs have considerable experience in the area of turbomachinery, and a number of industrial contacts. The results of the research will be shared with representatives from aircraft engine manufacturers, and it is anticipated that the work on absorbers will be guided in part by considerations raised during discussions with them. Overall, the goal will be to transfer the basic knowledge gained by this research into the classroom, to young aspiring engineers, and to industry.
