The subspace iteration method for eigenproblems of frames with viscoelastic dampers described using internal variables

• Autorzy: Łasecka-Plura Magdalena

Identyfikatory

DOI

10.21008/j.0860-6897.2020.3.13

• Języki publikacji: EN

Abstrakty

EN

In the paper, the subspace iteration method is used to solve quadratic eigenproblems written for structures with viscoelastic dampers. This allows a certain previously assumed number of eigenvalues and corresponding eigenvectors to be determined. A shear frame with mass lumped on the storey level with built-in dampers is considered. Dampers are modelled with the classical Zener model. Equations of motion are written in the matrix form and include the internal variables resulting from built-in dampers. The subspace iteration method starts from adopting the number of sought solution for the quadratic eigenproblem, then the starting point of the iteration is determined and the iterative procedure is initiated. In each iterative loop the reduced quadratic eigenproblem with Hermitian matrices is solved by rearranging it into a state space form.

Słowa kluczowe

EN

subspace iteration method; Hermitian quadratic eigenproblem; dampers; Zener model

PL

metoda iteracji podprzestrzeni; amortyzator; model Zenera

• Wydawca: Poznan University of Technology. Institute of Applied Mechanics
• Czasopismo: Vibrations in Physical Systems
• Rocznik: 2020
• Tom: Vol. 31, nr 3
• Strony: art. no. 2020313
• Opis fizyczny: Bibliogr. 8 poz., rys.

Twórcy

autor

Łasecka-Plura Magdalena

• Institute of Structural Analysis, Poznan University of Technology ul. Piotrowo 5, 60-965 Poznań

Bibliografia

• 1. C. Lanczos, An iteration method for the solution of the eigenvalue problem of linear differential and integral operators, J Res Natl Bur Stand, 45 (1950) 255-282.
• 2. W.E. Arnoldi, The principle of minimized iterations in the solution of the matrix eigenvalue problems, Q Appl Math, 9 (1951) 17-29.
• 3. K.J. Bathe, Finite Element Procedures, Prentice Hall, New Jersey 1996.
• 4. A.Y.T. Leung, Subspace iteration for complex symmetric eigenproblems, J Sound Vib, 184 (1995) 627-637.
• 5. P. Fischer, Eigensolution of nonclassically damped structures by complex subspace iteration, Comp Method Appl M, 189 (2000) 149-166.
• 6. M. Łasecka-Plura, R. Lewandowski, Application of the subspace iteration method to solve the nonlinear eigenproblem for systems with viscoelastic dampers, 4th Polish Congress of Mechanics and 23rd International Conference on Computer Methods in Mechanics PCM-CMM-2019, Kraków, Poland, September 8-12, 2019.
• 7. R. Lewandowski, A. Bartkowiak, H. Maciejewski, Dynamic analysis of frames with viscoelastic dampers: a comparison of dampers models, Struct Eng Mech, 41 (2012) 113-137.
• 8. R. Lewandowski, Vibration reduction of building structures, PWN, Warsaw 2014 (in Polish).

Uwagi

Opracowanie rekordu ze środków MNiSW, umowa Nr 461252 w ramach programu "Społeczna odpowiedzialność nauki" - moduł: Popularyzacja nauki i promocja sportu (2021).