Basis Vector Quantification of Flutter Analysis Structural Modes

Abstract

Amethodto conciselyquantify, compare, andidentify mode shapesfor flutter analysisusingorthogonalized basis vectors is developed. The procedure numerically describes wing structural mode shapes as scalar projections onto a reduced set of basis vectors. The basis vectors are baseline wing shapes derived from the mode shapes of a reference wing model, and mode shapes from other wing models are concisely related to the basis vectors using the scalar projections. The resulting quantifier describes the wing modes in terms of the physical wing shapes from the reference model. The technique is demonstrated on a simple wing model from which the basis vectors are derived. Masselementsareaddedtothewinginfourdifferentconfigurationstoproducevariousmodeshapesforcomparison tothebasisset.Thesemodeshapesarequantifiedinterms ofbasisvectorcomponentsthatareexpressedconciselyin matrixform.Visualcomparisonsofthemodeshapestothebasisvectorsshowthatthenumericcharacterizationsare consistent with the visual interpretations. Comparison of the four configurations to one another indicates that the numeric components distinguish subtle differences in wing deformation as well as differences in the overall shape of the deformed wing.