5. CONCLUSIONS While Guyan continues to be widely utilized for definition of test-analysis models (TAMs), modern 3-D elastic and other advanced models have introduced serious deficiencies in its application. Specifically, inappropriate Rayleigh-Ritz trial vectors result from implied point unit loads associated with Guyan Reduction. This paper introduces a new, systematic strategy for definition of reduced finite element structural dynamic models, employing trial vectors associated with distributed load patches. The new method closely follows the Guyan Reduction principle and it appears to produce more accurate reduced models in situations that are both appropriate and problematic for classical Guyan Reduction. A key feature of the new method is its natural definition of centroidal, “average” displacements associated with systematically defined, distributed load patches. This feature leads to definition of straightforward TAMs that should be especially advantageous in test-analysis correlation evaluations of shell-type structures. In addition, in the case of a symmetric shell-type structure, the new reduction strategy permits computation of accurate (almost exact) overall body modes, while ignoring the many breathing modes (in the same frequency band as body modes), The new load-patch reduction method must be subjected to further studies and evaluations in order to uncover the extent and limitations of its utility. REFERENCES [1] Harris’ Shock and Vibration Handbook, 6th Ed, A. Piersol and T. Paez (Ch. 23, R. Coppolino), McGraw-Hill, 2010 [2] The Finite Element Method: Its Basis and Fundamentals, 6th Ed, O. Zienkiewicz, R. Taylor, and J. Zhou, Elsevier,2005 [3] "Über eine neue Methode zur Lösung gewisser Variationsprobleme der mathematischen Physik”, W. Ritz, J. reine angew. Math. 135, 1-61, 1908. [4] “Reduction of Stiffness and Mass Matrices”, R. Guyan, AIAA Journal, Vol. 3, 1965 [5] “Coupling of Substructures for Dynamic Analysis”, R. Craig and M. Bampton, AIAA Journal, Vol. 6, July 1968 [6] “Large Eigenvalue Problems in Dynamic Analysis”, K-J Bathe and E. Wilson, ASCE J. Eng. Mech. Div 98(6), 1972 [7] The Lanczos Method Evolution and Application, L. Komzsik, Cambridge University Press, 1987 [8] “Automated Response DOF Selection for Mapping of Experimental Normal Modes”, R. Coppolino, IMAC XVI, 1998 [9] “A Procedure for an Improved Reduced System (IRS) Model, J. O’Callahan, IMAC VII, 1989 [10] History of Strength of Materials, S. Timoshenko, Dover Publications, 1983 [11] Conversations, during the mid 1980’s, with Robert T. Lahey, who had previously developed and applied a load patch procedure at Lockheed Aircraft Company. 366
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