4 K. Truong and P. Avitabile 2 Leading Edge Shear Web Trailing Edge Shear Web Spar Cap Skin DETAILED MODEL SIMPLE BEAM REPRESENTATION Fig. 1.2 Generation of a simplistic beam model from a detailed composite ply configuration The transformation matrix [T] is used to project the full mass and stiffness matrices to a smaller size. The reduced matrices can be formulated as ŒMa DŒT T ŒMn ŒT (1.2) ŒKa DŒT T ŒKn ŒT (1.3) For model reduction, it is important that the eigenvalues and eigenvectors of the original system are preserved as accurately as possible in the reduction process. If this is not maintained then the matrices are of questionable value. The eigensolution is then given by ŒŒKa œŒMa fXagDf0g (1.4) Because reduction schemes such as Guyan Condensation [1] and Improved Reduced System Technique [2] are based primarily on the stiffness of the system, the eigenvalues and eigenvectors will not be exactly reproduced in the reduced model. However, the System Equivalent Reduction Expansion Process (SEREP) [3] exactly preserves the eigenvalues and eigenvectors in the reduced model. 1.2.2 System Equivalent Reduction Expansion Process (SEREP) For the specific work in this paper, the SEREP has been used to make the reduced order models. SEREP produces reduced matrices for mass and stiffness that yield the exact frequencies and mode shapes as those obtained from the eigensolution of the full size matrix. The SEREP transformation is formed as ŒTU DŒUn ŒUa g (1.5) with ŒUa g Dh UT a Ua 1UT a i (1.6)
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