Symmetry Approach to Extension of Flutter Boundaries via Mistuning
Shapiro, B. Symmetry Approach to Extension of Flutter Boundaries via Mistuning. Journal of Propulsion and Power, vol14, no3, pg354-366, May-June 1998.
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A 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.