MODEL UPDATING USING CONSTRAINED EIGENSTRUCTURE ASSIGNMENT

A technique of constrained eigenstructure assignment (CEA) is presente d. The technique can update small order finite element models by using experimental modal analysis data or assign analytical eigenstructure to dynamic models for purposes of simulation and design. The CEA techn ique forms symmetric damping and stiffness correction matrices that mi rror the form of the existing model. Non-zero entries in the upper tri angular parts of the correction matrices become design variables and a re optimized to assign the desired eigenstructure. A common problem in updating methods is the loss of physical connectivity and matrix symm etry. The method proposed here retains matrix symmetry and banding, an d the signs of the diagonal and off-diagonal elements, and can bound t he magnitude of any entries of the coefficient matrices. Furthermore, the method can maintain the identities between repetitive entries in t he matrices that occur due to symmetries in the geometry of the model. This is important when identical sections of a model should have iden tical stiffness and damping in the updated model. Also, this repetitiv eness can substantially reduce the computational time of the solution. The CEA technique also incorporates an optional eigenvector iteration feature that minimizes shifting of unassigned eigenvalues. This is im portant for design purposes and when assigning only a few measured eig envalues to the analytical model. A computer algorithm completely cont ained within the framework of the Matlab software system has been deve loped to implement the method. Simple example problems are presented t o exhibit the utility of the technique. Note that the method presented here is most applicable to small or reduced order dynamic models, as large dimensions render the computations very slow.