# Jiashang Jiang

## Publications

##### 5 An Efficient Iterative Updating Method for Damped Structural Systems

**Authors:**
Jiashang Jiang

**Abstract:**

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.

**Keywords:**
Model Updating,
iterative algorithm,
Optimal approximation,
damped structural
system

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

**Authors:**
Jiashang Jiang,
Yongxin Yuan

**Abstract:**

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.

**Keywords:**
Model Updating,
Partially prescribed spectral information,
damped gyroscopic system

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

**Authors:**
Yongxin Yuan,
Jiashang Jiang

**Abstract:**

**Keywords:**
Parameter Estimation,
iterative algorithm,
Matrix Equation,
minimum norm solution

##### 2 Iterative Solutions to Some Linear Matrix Equations

**Authors:**
Jiashang Jiang,
Hao Liu,
Yongxin Yuan

**Abstract:**

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.

**Keywords:**
Parameter Estimation,
iterative algorithm,
Matrix Equation,
minimum norm solution

##### 1 A New Direct Updating Method for Undamped Structural Systems

**Authors:**
Yongxin Yuan,
Jiashang Jiang

**Abstract:**

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.

**Keywords:**
Model Updating,
finite element model,
Optimal approximation,
modal data