Model Updating in Symmetric Positive Semi-definite Models using Incomplete Measured Data

To have a more complete description of the problem, access here .

Here a computer program is provided. To directly run this program, acess here.

Suppose that symmetric matrices $M \in {\mathbb{R}}^{n \times n}$, $K \in {\mathbb{R}}^{n \times n}$, are given such that the undamped model $(M,D,K)$, where $D = 0$, has eigenstructure sets $(\Lambda_1,X_1)$ and $(\Lambda_2,X_2)$ (in compact representation) such that

Our purpose is to compute a symmetric matrix $\Phi \in {\mathbb{R}}^{m \times m}$ such that the symmetric matrix
$\displaystyle \tilde{K} = K - M X_1 \Phi X_1^T M $
is such that the new symmetric undamped model $(M,D,\tilde{K})$, where $D = 0$, incorporates the information from the vibration test, without changing the unknown frequencies and mode shapes represented by $(\Lambda_2,X_2)$, that is, we do not allow spill-over to occur.

Here, we provide a computer program to compute this matrix $\Phi$, 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 $\Lambda_1^2$ to compute $\Phi$, the eigenvalue matrix must still be provided in order to compute the quantity

$\displaystyle \Vert M X_1 \Lambda_1^2 + K X_1 \Vert _F$
corresponding to a compatibility requirement.

Here a computer program is provided. To run this program, acess here.

Joao Carvalho 2006-03-17