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Research Papers

Riccati Transfer Matrix Method for Linear Tree Multibody Systems

[+] Author and Article Information
Junjie Gu

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

Xiaoting Rui

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

Jianshu Zhang

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

Gangli Chen

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

Qinbo Zhou

Institute of Launch Dynamics,
Nanjing University of Science and Technology,
Nanjing 210094, China
e-mail: zqb912_new@163.com

1Corresponding author.

Contributed by the Applied Mechanics Division of ASME for publication in the JOURNAL OF APPLIED MECHANICS. Manuscript received August 10, 2016; final manuscript received September 29, 2016; published online October 24, 2016. Editor: Yonggang Huang.

J. Appl. Mech 84(1), 011008 (Oct 24, 2016) (7 pages) Paper No: JAM-16-1399; doi: 10.1115/1.4034866 History: Received August 10, 2016; Revised September 29, 2016

The Riccati transfer matrix method (RTMM) improves the numerical stability of analyzing chain multibody systems with the transfer matrix method for multibody systems (MSTMM). However, for linear tree multibody systems, the recursive relations of the Riccati transfer matrices, especially those for elements with multiple input ends, have not been established yet. Thus, an RTMM formulism for general linear tree multibody systems is formulated based on the transformation of transfer equations and geometrical equations of such elements. The steady-state response under harmonic excitation of a linear tree multibody system is taken as an example and obtained by the proposed method. Comparison with the finite-element method (FEM) validates the proposed method and a numerical example demonstrates that the proposed method has a better numerical stability than the normal MSTMM.

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References

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Figures

Grahic Jump Location
Fig. 1

Linear tree multibody system: (a) beam-body example and (b) computational process by RTMM

Grahic Jump Location
Fig. 2

Steady-state mode shape of the system

Grahic Jump Location
Fig. 3

Variation trend of Y¯(Ω) w.r.t. Ω

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