Model Updating in Symmetric Positive Semi-definite Models using Incomplete Measured Data
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Suppose that symmetric matrices
, are given such that
the undamped model , where , has eigenstructure sets
(in compact representation) such that
Our purpose is to compute a symmetric matrix
such that the symmetric matrix
is such that the new symmetric undamped model
, where ,
incorporates the information from the vibration test, without changing the
unknown frequencies and mode shapes represented by
, that is,
we do not allow spill-over to occur.
- the first, satisfying
is a diagonal matrix with non-positive
entries (eigenvalue matrix),
corresponding eigenvector matrix,
represent part of the eigenstructure which we want to update, to which the
vibration test gives measured data matrices
(only first entries of corresponding mode shapes
- the last, satisfying
, the eigenvector matrix, represent an unknown part of the eigenstructure which we want to not get changed.
Here, we provide a computer program to compute this matrix , following
an algorithm given in J. Carvalho, State Estimation and Finite-Element
Model Updating in Vibrating Systems, PhD. Dissert, NIU, 2002.
Although the algorithm itself does not require direct information on
to compute , the eigenvalue matrix must still be provided
in order to compute the quantity
corresponding to a compatibility requirement.
Here a computer program is provided. To run this program, acess