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A new updating method for the damped mass-spring systems. (English) Zbl 1460.70017
Summary: 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.

MSC:
70J35 Forced motions in linear vibration theory
65L09 Numerical solution of inverse problems involving ordinary differential equations
65L15 Numerical solution of eigenvalue problems involving ordinary differential equations
34A55 Inverse problems involving ordinary differential equations
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