Fast Flutter Uncertainty Calculation Based on Arbitrary Mode Shapes and Reduced - Order Modeling

A new method for calculating flutter characteristics is presented using Arbitrary basis mode shapes and reduced-order modeling (ROM) techniques. It can be applied to aeroelastic uncertainty analysis efficiently and accurately, without recalculation of normal modes and aerodynamic force though structural parameters vary. First, a number of normal mode shapes of different structure samples is calculated by changing the baseline structural parameters, such as mass or stiffness variations. Then the reduced arbitrary basis mode shapes are extracted from the above mode shape samples using the principal component analysis (PCA) method. Therefore, the physical mode shapes of varied structures can be regarded as linear combination of the reduced arbitrary basis mode shapes. Hence, under the coordinate system of reduced arbitrary basis mode shapes, there is no need to recalculate the physical normal mode shapes when structure parameters vary. The Modal Assurance Criterial (MAC) is used to evaluate the accuracy of normal mode shapes represented by the reduced arbitrary basis modes. Afterwards, the generalized aerodynamic force coefficients under the dynamic motion of arbitrary basis mode is calculated by the CFD technique, which is identified to a reduced-order model by the observer method. Finally, in order to perform flutter analysis with aerodynamic reduced-order model under the coordinates of arbitrary basis mode, the uncertain aeroelastic equation is deduced under the new coordinate system, to consider the structural variations. Flutter analysis and uncertainty quantification is conducted on a flat plate by the polynomial chaos expansion (PCE). Compared with the Monte Carlo Simulation, results indicate that this method with ROM and PCE is accurate and much more efficient.