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Dynamic modeling of a flexible beam with large overall motion and nonlinear deformation using the finite element method

## Dynamic modeling of a flexible beam with large overall motion and nonlinear deformation using the finite element method

He Xing-Suo, Deng Feng-Yan, Wu Gen-Yong, Wang Rui
• #### Abstract

In this paper, the dynamic modeling theory of a flexible beam, which incorporates large overall motion and nonlinear deformation, is investigated. As we knows, in spacecraft and space station, there are a lot of flexible appendices, the dynamic modeling of a flexible beam is essential. Yet existing such models, in our opinion, lack several important coupling terms. This paper supplies these important coupling terms. It is reasonable to use geometrically nonlinear deformation fields to demonstrate and simplify a flexible beam undergoing large overall motion. In this paper, the finite element method is used for the system discretization and the coupling dynamic equations of flexible beam are obtained by Lagrange’s equations. The complete expression of stiffness matrix and all coupling terms are included in the dynamic equations. The second order coupling terms among rigid large overall motion, arc length stretch, lateral flexible deformation kinematics and torsional deformation terms are concluded in the present exact coupling model to expand the theory of one-order coupling model. The dynamic properties of a planar flexible rotating beam in the non-inertial reference frame are developed.

• Funds:

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•  Citation:
##### Metrics
• Abstract views:  3129
• Cited By: 0
##### Publishing process
• Received Date:  13 January 2009
• Accepted Date:  09 April 2009
• Published Online:  15 January 2010

## Dynamic modeling of a flexible beam with large overall motion and nonlinear deformation using the finite element method

• 1. 西北工业大学工程力学系，西安 710072

Abstract: In this paper, the dynamic modeling theory of a flexible beam, which incorporates large overall motion and nonlinear deformation, is investigated. As we knows, in spacecraft and space station, there are a lot of flexible appendices, the dynamic modeling of a flexible beam is essential. Yet existing such models, in our opinion, lack several important coupling terms. This paper supplies these important coupling terms. It is reasonable to use geometrically nonlinear deformation fields to demonstrate and simplify a flexible beam undergoing large overall motion. In this paper, the finite element method is used for the system discretization and the coupling dynamic equations of flexible beam are obtained by Lagrange’s equations. The complete expression of stiffness matrix and all coupling terms are included in the dynamic equations. The second order coupling terms among rigid large overall motion, arc length stretch, lateral flexible deformation kinematics and torsional deformation terms are concluded in the present exact coupling model to expand the theory of one-order coupling model. The dynamic properties of a planar flexible rotating beam in the non-inertial reference frame are developed.

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