Aerospace Engineering Research Works
Permanent URI for this collectionhttp://hdl.handle.net/1903/1655
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Item Symmetry Approach to Extension of Flutter Boundaries via Mistuning(American Institute of Aeronautics and Astronautics, 1998-05) Shapiro, BenjaminA general framework is presented for analyzing and optimizing stability increases resulting from mistuning. The framework given is model independent and is based primarily on symmetry arguments. Difficult practical issues are transformed to tractable mathematical questions. It is shown that mistuning analysis reduces to a block circular matrix eigenvalue/vector problem that can be solved efficiently even for large problems. Similarly, the optimization becomes a standard linear constraint quadratic programming problem and can be solved numerically. Because the methods given are model-independent, they can be applied to various models and allow the researcher to easily conclude which models accurately capture mistuning and which do not. A simple quasisteady model for flutter in a cascade is used to illustrate and validate results in this paper.Item Solving for Mistuned Forced Response by Symmetry(American Institute of Aeronautics and Astronautics, 1999-03) Shapiro, BenjaminThe introduction of mistuning in jet-engine bladed disks can lead to large changes in stability and forced response. Even small random mistuning (within the bounds of manufacturing tolerance) can lead to unacceptable response and high-cycle fatigue. Meanwhile, intentional mistuning may improve stability and forced response under manufacturing uncertainty. This paper presents a general framework for predicting forced response as a function of mistuning. Because the forced response problem is an almost singular linear problem, its solution is highly nonlinear in the mistuning parameters. Our methods exploit symmetry arguments and eigenstructure perturbation to provide a method valid for any model. It is shown that, by perturbing eigenvectors in the numerator and the inverse of eigenvalues in the denominator (exploiting symmetry in both computations), we can accurately approximate the forced response as a function of mistuning. Results are demonstrated for a simple lightly damped model, and the consequent sharp nonlinear behavior is captured almost perfectly. We also show that intentional mistuning may guarantee improved stability and forced response under fixed manufacturing tolerances. Thus, intentional mistuning should be considered as a practical means of increasing safety and enhancing engine performance.Item Analyzing Mistuning of Bladed Disks by Symmetry and Reduced-Order Areodynamic Modeling(American Institute of Aeronautics and Astronautics, 2003-03) Shapiro, Benjamin; Willcox, KarenThe mistuned behavior of bladed disks is analyzed and optimized using an unsteady, transonic, computational fluid dynamic model (CFD). This result is enabled by the integration of two frameworks: the first is based on symmetry arguments and an eigenvalue/vector perturbation scheme, while the second is a reduction technique based on the proper orthogonal decomposition (POD). The first framework reduces the complexity of the problem, reveals engineering trade offs and suggests the existence of an intentional robust mistuning which improves both stability and forced response with respect to random variations in blade parameters. The second framework permits the reduction of state-of-the-art computational fluid dynamic codes to reduced-order models, which capture the accuracy of the original simulation but fit within the mistuning analysis framework. Together, these methodologies allow the analysis of a transonic, bladed disk with stiffness mistuning (see Fig. 1).Moreover, because of the low order of the aeroelasticmodel, a robust control¹ uncertainty analysis can be used to prove that the intentional mistuning suggested by the symmetry analysis framework is indeed robust. Hence this paper contains the first rigorous demonstration that intentional mistuning can robustly improve both the stability and forced response for a model that includes sophisticated aerodynamic effects.