Tools for the Analysis and Optimization of Frequency Response Functions in Systems with Symmetry

Prof. Mario Rotea, School of Aeronautics and Astronautics, Purdue University

The prediction and optimization of frequency response functions for systems with high modal density and low damping is of great interest to the manufacturers of modern gas turbine aeroengines. This interest is motivated in part by a need to analyze and optimize vibratory responses in new compressor rotor designs which, to realize weight and aerodynamic benefits, are becoming more and more structurally flexible and exhibit large number of vibration modes in the operating envelope. Since 1998, we have been working with Pratt and Whitney in the development of metrics and effective tools to analyze and optimize real-world rotors. These systems typically posses a degree of spatial symmetry that can be exploited to develop improved methods and tools for analysis and design.

In this talk, we will describe a problem-specific algorithm for the efficient calculation of worst-case frequency responses. Technically, the problem is that of maximizing a nonlinear function of unknown parameters or perturbations given a model of the system. Due to the large number of parameters, on the order of hundreds for real rotors, general-purpose algorithms are computationally expensive and do not run in practical times. We will show that utilization of the underlying problem structure leads to an algorithm whose cost is O(N) smaller than the cost of general-purpose algorithms, where N is the number of parameters. This result indicates a cost reduction proportional to N, which for problems with hundreds of parameters is not trivial. The algorithm will be illustrated on the problem of calculating the manufacturing tolerances required for acceptable forced response in bladed rotors. The algorithm will also be used to quantify the increased robustness [e.g., reduced sensitivity to manufacturing variations] achieved by partially symmetric rotors. The talk should appeal to a broad audience including those interested in conducting sensitivity and worst-case tolerance analysis in systems with spatial patterns.