A new updating method for the damped mass-spring systems |
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Institution: | 1. College of Science, National University of Defense Technology, Changsha 410073, PR China;2. School of Mathematics and Statistics, Changsha University of Science and Technology, Changsha 410114, PR China;3. College of Mathematics and Econometrics, Hunan University, Changsha 410082, PR China |
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Abstract: | 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, nonnegativity of stiffness and the physical connectivity of the original model are preserved. Numerical results show that our proposed method works well. |
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