5

5

8105

Iterative Solutions to Some Linear Matrix Equations

In this paper the gradient based iterative algorithms are presented to solve the following four types linear matrix equations: (a) AXB = F; (b) AXB = F, CXD = G; (c) AXB = F s. t. X = XT ; (d) AXB+CYD = F, where X and Y are unknown matrices, A,B,C,D, F,G are the given constant matrices. It is proved that if the equation considered has a solution, then the unique minimum norm solution can be obtained by choosing a special kind of initial matrices. The numerical results show that the proposed method is reliable and attractive.

Matrix equation, iterative algorithm, parameter estimation, minimum norm solution.

4

10047

The Direct Updating of Damping and Gyroscopic Matrices using Incomplete Complex Test Data

In this paper we develop an efficient numerical method for the finite-element model updating of damped gyroscopic systems based on incomplete complex modal measured data. It is assumed that the analytical mass and stiffness matrices are correct and only the damping and gyroscopic matrices need to be updated. By solving a constrained optimization problem, the optimal corrected symmetric damping matrix and skew-symmetric gyroscopic matrix complied with the required eigenvalue equation are found under a weighted Frobenius norm sense.

Model updating, damped gyroscopic system, partially prescribed spectral information.

3

11823

A New Direct Updating Method for Undamped Structural Systems

A new numerical method for simultaneously updating mass and stiffness matrices based on incomplete modal measured data is presented. By using the Kronecker product, all the variables that are to be modified can be found out and then can be updated directly. The optimal approximation mass matrix and stiffness matrix which satisfy the required eigenvalue equation and orthogonality condition are found under the Frobenius norm sense. The physical configuration of the analytical model is preserved and the updated model will exactly reproduce the modal measured data. The numerical example seems to indicate that the method is quite accurate and efficient.

Finite element model, model updating, modal data, optimal approximation.

2

12577

Iterative solutions to the linear matrix equation AXB + CXTD = E

In this paper the gradient based iterative algorithm is
presented to solve the linear matrix equation AXB +CXTD = E,
where X is unknown matrix, A,B,C,D,E are the given constant
matrices. It is proved that if the equation has a solution, then the
unique minimum norm solution can be obtained by choosing a special
kind of initial matrices. Two numerical examples show that the
introduced iterative algorithm is quite efficient.

matrix equation, iterative algorithm, parameter estimation,minimum norm solution.

1

10003362

An Efficient Iterative Updating Method for Damped Structural Systems

Model updating is an inverse eigenvalue problem which concerns the modification of an existing but inaccurate model with measured modal data. In this paper, an efficient gradient based iterative method for updating the mass, damping and stiffness matrices simultaneously using a few of complex measured modal data is developed. Convergence analysis indicates that the iterative solutions always converge to the unique minimum Frobenius norm symmetric solution of the model updating problem by choosing a special kind of initial matrices.

Model updating, iterative algorithm, damped structural
system, optimal approximation.