Summary
A new method of calculating the flutter boundaries of undamped aeroelastic “typical section” models is presented. The method is an application of the weak transversality theorem used in catastrophe theory. In the first instance, the flutter problem is cast in matrix form using a frequency domain method, leading to an eigenvalue matrix. The characteristic polynomial resulting from this matrix usually has a smooth dependence on the system's parameters. As these parameters change with operating conditions, certain critical values are reached at which flutter sets in. Our approach is to use the transversality theorem in locating such flutter boundaries using this criterion:at a flutter boundary, the characteristic polynomial does not intersect the axis of the abscissa transversally. Formulas for computing the flutter boundaries of structures with two degrees of freedom are presented, and extension to multi degree of freedom systems is indicated. The formulas have obvious applications in, for instance, problems of panel flutter at supersonic Mach numbers. Substantial savings in computation resources are possible when this non-iterative method is used, compared to existing frequency domain methods which are essentially iterative.
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Afolabi, D. Flutter analysis using transversality theory. Acta Mechanica 103, 1–15 (1994). https://doi.org/10.1007/BF01180214
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DOI: https://doi.org/10.1007/BF01180214