An inverse eigenvalue problem in symmetric sparse quadratic model updating

被引：0
作者：
Suman Rakshit
机构：
[1] Mankar College,Department of Mathematics
来源：
Computational and Applied Mathematics | 2021年 / 40卷
关键词：
Symmetric sparse matrix; Quadratic model; Inverse eigenvalue problem; Model updating problem; 15A22; 15A18; 65F18;
D O I：
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学科分类号：
摘要：
In this paper, symmetric sparse quadratic model updating problem (SSQMUP) is considered from the perspective of an inverse eigenvalue problem. This problem attempts to update the analytical model (stiffness and damping matrices), so that it agrees with the measured eigendata and preserves the symmetric and sparsity structure of the original model. In this paper, a necessary and sufficient condition for the existence of solution of SSQMUP is derived. In addition, we present the expressions of the class of all solutions to this problem explicitly. Moreover, we proposed an optimization-based approach to find the solution of this problem which is nearest to the analytical model. Validity of the our proposed method is illustrated with results on numerical experiments on a spring mass problem.
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  • [1] Bai ZJ(2007)Symmetric tridiagonal inverse quadratic eigenvalue problems with partial eigendata Inverse Problems 24 015005-603
  • [2] Cai J(2018)Least-squares solutions of generalized inverse eigenvalue problem over Hermitian–Hamiltonian matrices with a submatrix constraint Comput Appl Math 37 593-864
  • [3] Chen J(2006)Symmetry preserving eigenvalue embedding in finite-element model updating of vibrating structures J Sound Vib 290 839-428
  • [4] Carvalho J(2008)Spillover phenomenon in quadratic model updating AIAA J 46 420-48
  • [5] Datta BN(1997)Orthogonality and partial pole assignment for the symmetric definite quadratic pencil Linear Algebra Appl 257 29-110
  • [6] Lin WW(2000)Partial eigen structure assignment for the quadratic pencil J Sound Vib 230 101-1772
  • [7] Wang CS(2009)An optimization technique for damped model updating with measured data satisfying quadratic orthogonality constraint Mech Syst Signal Process 23 1759-2338
  • [8] Chu MT(2014)A new multi-objective approach to finite element model updating J Sound Vib 333 2323-2493
  • [9] Datta BN(2012)Quadratic model updating with no spill-over and incomplete measured data: existence and computation of solution Linear Algebra Appl 436 2480-1316
  • [10] Lin WW(2006)New methods for finite element model updating problems AIAA J 44 1310-301
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