An inverse eigenvalue problem for the finite element model of a vibrating rod
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摘要
An inverse eigenvalue problem for the finite element model of a longitudinally vibrating rod whose one end is fixed and the other end is supported on a spring is considered. It is known that the mass and stiffness matrices are both tridiagonal for the finite element model of the rod based on linear shape functions. It is shown that the cross section areas can be determined from the spectrum of the rod. The inverse vibration problem can be recast into an inverse eigenvalue problem of a special Jacobi matrix. The necessary and sufficient conditions for the construction of a physically realizable rod with positive cross section areas are established. A numerical method is presented and an illustrative example is given.
论文关键词:15A18,65F15,65F18,Eigenvalue,Inverse problem,Rod,Finite element model
论文评审过程:Received 3 December 2013, Revised 10 November 2015, Available online 8 January 2016, Version of Record 21 January 2016.
论文官网地址:https://doi.org/10.1016/j.cam.2015.12.038