Numerical Methods For Solving Structural Dynamics Model Updating Problems

With the development of computer technology and the complexity of the engineering structure,finite element model updating has become an indispensable technology for engineering analysis of structural systems.This paper mainly studies the finite element model updating problems of the damped gyroscopic structural system,and provides mathematical theory and effective numerical methods for these problems.The full text is as follows.For the MDGKN-system,a direct matrix updating method is proposed.Under the assumption that the mass matrix is accurate,By using the QR-decomposition of the measured modal matrix and the matrix derivative,the symmetric damping matrix,symmetric stiffness matrix,anti-symmetric gyroscopic matrix and anti-symmetric dissipation matrix which satisfy the characteristic equation are obtained.Also,the optimal approximation damping,stiffness,gyroscopic and dissipation matrices are obtained under the Frobenius norm sense.For the MDKN-system,a direct matrix updating method is presented.By using the QR-decomposition of the modal matrix,kronecker product,straightening operator and matrix derivative,the symmetric mass matrix,symmetric damping matrix,symmetric stiffness matrix and anti-symmetric dissipation matrix satisfying the characteristic equation are obtained.Furthermore,using the matrix optimal approximation theory,the optimal approximation mass,damping,stiffness and dissipation matrices are also obtained.For the MDGK-system,a finite iterative updating method is proposed.By the method,the optimal approximation symmetric mass matrix,symmetric damping matrix,symmetric stiffness matrix and anti-symmetric gyroscopic which satisfy the required characteristic equation can be obtained within finite iteration steps in the absence of roundoff errors by choosing a special kind of initial matrix group.In order to verify the effectiveness of the proposed method,numerical algorithms and the corresponding numerical examples for solving these problems are given.The numerical results show that the proposed method is reliable and effective.