A new updating method for the damped mass-spring systems

作者：Zhao, Kang^*; Cheng, Lizhi; Li, Shengguo; Liao, Anping

来源：Applied Mathematical Modelling, 2018, 62: 119-133.

DOI：10.1016/j.apm.2018.05.024

• Inverse eigenvalue problem
• Alternating direction method
• Polynomial optimization problem
• Model updating
• Mass-spring system

In this paper, we concern the inverse problem of constructing a monic quadratic pencil which possesses the prescribed partial eigendata, and the damping matrix and stiffness matrix are symmetric tridiagonal. Furthermore, the stiffness matrix is positive semi-definite and weakly diagonally dominant, which has positive diagonal elements and negative off-diagonal elements. Based on the solution of the inverse eigenvalue problem, we apply the alternating direction method with multiplier to solve the finite element model updating problem for the serially linked mass-spring system. The positive semi-definiteness of stiffness matrix, non-negativity of stiffness and the physical connectivity of the original model are preserved. Numerical results show that our proposed method works well.

• 出版日期2018-10
• 单位中国人民解放军国防科学技术大学; 长沙理工大学; 湖南大学