59126 - Numerical Methods for Calculating Component Modes for Geometric Mistuning Reduced-Order Models 

Geometric mistuning models formulated from a component mode synthesis methods often require the calculation of component modes, particularly constraint and fixed interface normal modes, during substructuring.  For Integrally Bladed Rotors, these calculations are required for each sector.  This paper proposes methods that reuse information garnered from solving the constraint modes of a single sector on the remaining sectors to reduce memory requirements and solution times. A mesh metamorphosis tool is used to ensure finite element models match geometry obtained from a 3D optical scanner.  This tool also produces a common mesh pattern from sector-to-sector.  This is exploited to produce common permutation matrices and symbolic factorizations of sector stiffness matrices that are proposed for reuse in solving subsequent constraint modes.  Furthermore, a drop tolerance is introduced to remove small values during constraint mode calculation to reduce memory requirements. It is proposed to reuse this dropping pattern produced from a single sector on the remaining sectors.  Approaches are then extended to a parallel processing scheme to propose effective matrix partitioning methods.  Finally, information gathered during the constraint mode calculations are reused during the solution of the fixed interface normal modes to improve solution time.  Results show reusing permutation matrices and symbolic factorizations from sector-to-sector improves solution time and introduces no error.  Using a drop tolerance is shown to reduce storage requirements of a constraint mode matrix.  Furthermore, it is shown that reusing the same dropping pattern introduces minimal error without degradation in solution times.  Finally, reusing the information from constraint modes for calculating fixed interface normal modes greatly improved the performance in a shift-and-invert technique for solving eigenvalue problems.