A d i r e c t i d e n t i f i c a t i o n procedure i s proposed t o o b t a i n the mass and s t i f f n e s s m a t r i c e s based on the t e s t measured eigenvalues and eigenvectors. The method i s based on t h e theory of m a t r i x p e r t u rb a t i o n i n which t h e c o r r e c t mass and s t i f f n e s s matrices a r e expanded i n terms of a n a l y t i c a l v a l u e s plus a modification matrix. The s i m p l i c i t y of t h e procedure enables r e a l time o p e r a t i o n during t h e s t r u c t u r a l t e s t i n g .
I n t r o d u c t i o nOne of t h e p r i n c i p a l o b j e c t i v e s of t h e modal t e s t i s t o v e r i f y t h e a n a l y t i c a l model by comparing t h e experimentally determined modal c h a r a c t e r i s t i c s such a s t h e n a t u r a l frequencies and mode shapes t o those obtained from t h e a n a l y t i c a l model.Frequently, t h e a n a l y t i c a l model does n o t i n i t i a l l y produce c h a r a c t e r i s t i c s t h a t concur with t e s t r e s u l t s , and consequently t h e a n a l y t i c a l model i s adjusted o r improved u n t i l t h e a n a l y s i s and t e s t r e s u l t s agree. With increasing complexity of t h e s t r u c t u r a l system, t h e model adjustment o r improvement becomes d i f f i c u l t and systematic approaches a r e necessary, (Refs. 1 and 2).One of the approaches i s based on t h e estimat i o n theory i n which t h e d i f f e r e n c e s between t h e measured and a n a l y t i c a l l y obtained eigenvectors and eigenvalues a r e used t o e s t i m a t e those model parame t e r s t h a t a f f e c t t h e s e q u a n t i t i e s .The essence of t h i s approach i s t h e establishment of the so-called "Jacobian Matrix" whose elements a r e t h e derivat i v e s of eigenvalues and modal displacements with r e s p e c t t o t h e parameters. These parameters can be t h e elements i n t h e mass matrix and the s t i f f n e s s of t h e s t r u c t u r a l members.Using the Jacobian Matrix the changes i n eigenvalues and eigenvectors a s f u n c t i o n s of parameter changes can be established.The most important advantage of t h e approach i s t h e r e t a i n i n g of physical meanings of estimated parameters.However, t h e approach i s an i t e r a t i v e procedure whose convergence may be slow and dependent on t h e s e l e c t i o n of parameters and t e s t measurements, (Ref. 3 ) . This method was applied on a r e a l i s t i c s t r u c t u r a l system, t h e Viking S p a c e c r a f t , with t e s t measured eigenvalues and e i g e n v e c t o r s , (Ref. 4 ) . I t demonstrated t h a t the convergence of t h e i t e r a t i o n procedure can be slow f o r c e r t a i n cases. On t h e o t h e r hand, methods have been developed t h a t mass and s t i f f n e s s m a t r i c e s can be d i r e c t l y i d e n t i f i e d by using t e s t measured eigenvectors and *Member of Technical S t a f f , AIAA Member **Supervisor, S t r u c t u r e s and Dynamics Technology Group, AIAA Member Index Ca...
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