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 , , are given such that the undamped model , where , has eigenstructure sets and (in compact representation) such that

• the first, satisfying , where is a diagonal matrix with non-positive entries (eigenvalue matrix), is the corresponding eigenvector matrix, represent part of the eigenstructure which we want to update, to which the vibration test gives measured data matrices and (only first entries of corresponding mode shapes are measured);
• the last, satisfying , where , , the eigenvector matrix, represent an unknown part of the eigenstructure which we want to not get changed.
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.

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 here.

Joao Carvalho 2006-03-17