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Research Papers

Study on the Stress-Stiffening Effect and Modal Synthesis Methods for the Dynamics of a Spatial Curved Beam

[+] Author and Article Information
Jianshu Zhang

Institute of Launch Dynamics,
Nanjing University of Science and Technology,
Nanjing 210094, China
e-mail: zhangdracpa@sina.com

Xiaoting Rui

Institute of Launch Dynamics,
Nanjing University of Science and Technology,
Nanjing 210094, China
e-mail: ruixt@163.net

Bo Li

Institute of Launch Dynamics,
Nanjing University of Science and Technology,
Nanjing 210094, China
e-mail: lbnjust@163.com

Gangli Chen

Institute of Launch Dynamics,
Nanjing University of Science and Technology,
Nanjing 210094, China
e-mail: chengangli1988@163.com

1Corresponding author.

Contributed by the Applied Mechanics Division of ASME for publication in the JOURNAL OF APPLIED MECHANICS. Manuscript received February 27, 2016; final manuscript received April 25, 2016; published online May 20, 2016. Editor: Yonggang Huang.

J. Appl. Mech 83(8), 081004 (May 20, 2016) (8 pages) Paper No: JAM-16-1111; doi: 10.1115/1.4033515 History: Received February 27, 2016; Revised April 25, 2016

In this paper, based on the nonlinear strain–deformation relationship, the dynamics equation of a spatial curved beam undergoing large displacement and small deformation is deduced using the finite-element method of floating frame of reference (FEMFFR) and Hamiltonian variation principle. The stress-stiffening effect, which is also called geometric stiffening effect, is accounted for in the dynamics equation, which makes it possible for the dynamics simulation of the spatial curved beam with high rotational speed. A numerical example is carried out by using the deduced dynamics equation to analyze the stress-stiffening effect of the curved beam and then verified by abaqus software. Then, the modal synthesis methods, which result in much fewer numbers of coordinates, are employed to improve the computational efficiency.

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Figures

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Fig. 2

Two-node beam element

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Fig. 1

A spatial curved beam and the coordinate systems

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Fig. 3

The undeformed configuration of the neutral axis of the curved beam

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Fig. 4

Results of FEMFFR and abaqus for scenario one: (a) endpoint deformation and (b) endpoint deformation velocity

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Fig. 5

Results of modal synthesis methods for scenario one: (a) endpoint deformation and (b) endpoint deformation velocity

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Fig. 6

Results for scenario two: (a) endpoint deformation and (b) endpoint deformation velocity

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