The subspace iteration method for nonlinear eigenvalue problems occurring in the dynamics of structures with viscoelastic elements
[ 1 ] Instytut Analizy Konstrukcji, Wydział Inżynierii Lądowej i Transportu, Politechnika Poznańska | [ 2 ] Instytut Konstrukcji Budowlanych, Wydział Budownictwa i Inżynierii Środowiska, Politechnika Poznańska | [ P ] pracownik | [ E ] pracownik emerytowany
2021
artykuł naukowy
angielski
- nonlinear eigenvalue problem
- subspace iteration method
- continuation method
- fractional derivatives
- viscoelastic material
EN The paper presents an extension of the subspace iteration method for application in systems with viscoelastic damping elements, which are described by both classical and fractional models. The presented method enables determination of only a certain number of eigenvalues and associated eigenvectors. This is very useful, especially when the considered problem has many degrees of freedom, in which case it would be very time-consuming or even impossible to determine all the eigenvalues. At the same time, from the engineering point of view, it is not necessary to know all the eigenvalues. In this paper, the subspace iteration method is used for the first time to solve the nonlinear eigenproblems which appear in the dynamic analysis of systems with viscoelastic damping elements. The proposed solution consists of assuming the number of eigenvalues to be determined, taking the initial point of iteration and then solving the nonlinear reduced eigenproblem with Hermitian matrices in each iterative loop. The solution to the reduced eigenproblem is obtained using the continuation method, and it is an additional novelty in the paper. The correctness and effectiveness of the proposed approach are illustrated with numerical examples.
03.06.2021
106571-1 - 106571-14
Article Number: 106571
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