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Symplectic perturbation series methodology for non-conservative linear Hamiltonian system with damping

Symplectic perturbation series methodology for non-conservative linear Hamiltonian system with... In this paper, the symplectic perturbation series methodology of the non-conservative linear Hamiltonian system is presented for the structural dynamic response with damping. Firstly, the linear Hamiltonian system is briefly introduced and its conservation law is proved based on the properties of the exterior products. Then the symplectic perturbation series methodology is proposed to deal with the non-conservative linear Hamiltonian system and its conservation law is further proved. The structural dynamic response problem with eternal load and damping is transformed as the non-conservative linear Hamiltonian system and the symplectic difference schemes for the non-conservative linear Hamiltonian system are established. The applicability and validity of the proposed method are demonstrated by three engineering examples. The results demonstrate that the presented methodology is better than the traditional Runge–Kutta algorithm in the prediction of long-time structural dynamic response under the same time step. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png "Acta Mechanica Sinica" Springer Journals

Symplectic perturbation series methodology for non-conservative linear Hamiltonian system with damping

"Acta Mechanica Sinica" , Volume 37 (6) – Jun 1, 2021

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References (45)

Publisher
Springer Journals
Copyright
Copyright © The Chinese Society of Theoretical and Applied Mechanics and Springer-Verlag GmbH Germany, part of Springer Nature 2021
ISSN
0567-7718
eISSN
1614-3116
DOI
10.1007/s10409-021-01076-0
Publisher site
See Article on Publisher Site

Abstract

In this paper, the symplectic perturbation series methodology of the non-conservative linear Hamiltonian system is presented for the structural dynamic response with damping. Firstly, the linear Hamiltonian system is briefly introduced and its conservation law is proved based on the properties of the exterior products. Then the symplectic perturbation series methodology is proposed to deal with the non-conservative linear Hamiltonian system and its conservation law is further proved. The structural dynamic response problem with eternal load and damping is transformed as the non-conservative linear Hamiltonian system and the symplectic difference schemes for the non-conservative linear Hamiltonian system are established. The applicability and validity of the proposed method are demonstrated by three engineering examples. The results demonstrate that the presented methodology is better than the traditional Runge–Kutta algorithm in the prediction of long-time structural dynamic response under the same time step.

Journal

"Acta Mechanica Sinica"Springer Journals

Published: Jun 1, 2021

Keywords: Symplectic perturbation series methodology; Non-conservative Hamiltonian system; Structural dynamic response; Symplectic difference scheme

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