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In this paper, the dynamic modeling theory of a spatial flexible beam, which undergoes large overall motion and nonlinear deformation, is investigated. As we know, in spacecraft and space station, there are a lot of flexible appendices so the dynamic modeling of a flexible beam is essential. Yet the existing models, in our opinion, lack several important coupling terms. This paper supplies these important coupling terms. Based on the new approach of deformation of fully geometrically nonlinear beam model developed，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 between rigid large overall motion, arc length stretch, lateral flexible deformation kinematics and torsional deformation terms are included in the present exact coupling model to expand the theory of one-order coupling model. The dynamic modeling method in this paper is of theoretical significance and has reference value for the rigid-flexible coupling system dynamic investigation .
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Keywords:
- large overall motion /
- nonlinear deformation /
- patial flexible beam /
- exact dynamic modeling
[1] ［1]Wang H B, Li J 2007 Acta Phys. Sin. 56 25041（in Chinese）［王洪波、李杰 2007 物理学报 56 2504］
[2] ［2]Liu Y Z 2009 Chin. Phys. B 18 1
[3] ［3]Zhang S Q 2008 Acta Phys. Sin. 57 1335（in Chinese）［张善卿 2008 物理学报 57 1335］
[4] ［4]Meng Z, Liu B 2008 Acta Phys. Sin. 57 1329（in Chinese）［孟宗、刘彬 2008 物理学报 57 1329］
[5] ［5]Xue Y, Weng D W 2009 Acta Phys. Sin. 58 34（in Chinese）［薛纭、翁德玮 2009 物理学报 58 34］
[6] ［6]Ge W K 2008 Acta Phys. Sin. 57 6714（in Chinese）［葛伟宽 2008 物理学报 57 6714］
[7] ［7]Jiang Z L, Hong J Z 1999 Journal of Vibration and Shock 18 10 （in Chinese）［蒋丽忠、洪嘉振 1999 振动与冲击 18 10］
[8] ［8]Deng F Y, He X S, Li L, Zhang J 2007 Multibody Syst Dyn . 18 559
[9] ［9]Liu C, Liu S X, Mei F X, Guo Y X 2008 Acta Phys. Sin. 57 6709（in Chinese）［刘畅、刘世兴、梅凤翔、郭永新 2008 物理学报 57 6709］
[10] ［10]Fu J L, Chen B Y, Tang Y F, Fu H 2008 Chin. Phys. B 17 3942
[11] ［11]Lin P, Fang J H, Pang T 2008 Chin. Phys. B 17 4361
[12] ［12]Liu J Y 2000 PhD thesis （Shanghai:Shanghai Jiaotong Uni.）（in Chinese）［刘锦阳 2000 博士毕业论文（上海:上海交通大学）］
[13] ［13]Yang H 2002 PhD thesis（Shanghai:Shanghai Jiao Tong Uni.）（in Chinese）［杨辉 2002 博士毕业论文,上海:上海交通大学］
[14] ［14]Lu Y F 1996 Dynamics of Flexible Multibody Systems （Beijing:Higher Education Press） （in Chinese）［陆佑方 1993 柔性多体系统动力学（高等教育出版社）］
[15] ［15]Mei F X, Xie J F, Jiang T Q 2008 Acta Phys. Sin. 57 4649（in Chinese）［梅凤翔、解加芳、江铁强 2008 物理学报 57 4649］
[16] ［16]Bai C L, Zhang X, Zhang L H 2009 Chin. Phys. B 18 475
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[1] ［1]Wang H B, Li J 2007 Acta Phys. Sin. 56 25041（in Chinese）［王洪波、李杰 2007 物理学报 56 2504］
[2] ［2]Liu Y Z 2009 Chin. Phys. B 18 1
[3] ［3]Zhang S Q 2008 Acta Phys. Sin. 57 1335（in Chinese）［张善卿 2008 物理学报 57 1335］
[4] ［4]Meng Z, Liu B 2008 Acta Phys. Sin. 57 1329（in Chinese）［孟宗、刘彬 2008 物理学报 57 1329］
[5] ［5]Xue Y, Weng D W 2009 Acta Phys. Sin. 58 34（in Chinese）［薛纭、翁德玮 2009 物理学报 58 34］
[6] ［6]Ge W K 2008 Acta Phys. Sin. 57 6714（in Chinese）［葛伟宽 2008 物理学报 57 6714］
[7] ［7]Jiang Z L, Hong J Z 1999 Journal of Vibration and Shock 18 10 （in Chinese）［蒋丽忠、洪嘉振 1999 振动与冲击 18 10］
[8] ［8]Deng F Y, He X S, Li L, Zhang J 2007 Multibody Syst Dyn . 18 559
[9] ［9]Liu C, Liu S X, Mei F X, Guo Y X 2008 Acta Phys. Sin. 57 6709（in Chinese）［刘畅、刘世兴、梅凤翔、郭永新 2008 物理学报 57 6709］
[10] ［10]Fu J L, Chen B Y, Tang Y F, Fu H 2008 Chin. Phys. B 17 3942
[11] ［11]Lin P, Fang J H, Pang T 2008 Chin. Phys. B 17 4361
[12] ［12]Liu J Y 2000 PhD thesis （Shanghai:Shanghai Jiaotong Uni.）（in Chinese）［刘锦阳 2000 博士毕业论文（上海:上海交通大学）］
[13] ［13]Yang H 2002 PhD thesis（Shanghai:Shanghai Jiao Tong Uni.）（in Chinese）［杨辉 2002 博士毕业论文,上海:上海交通大学］
[14] ［14]Lu Y F 1996 Dynamics of Flexible Multibody Systems （Beijing:Higher Education Press） （in Chinese）［陆佑方 1993 柔性多体系统动力学（高等教育出版社）］
[15] ［15]Mei F X, Xie J F, Jiang T Q 2008 Acta Phys. Sin. 57 4649（in Chinese）［梅凤翔、解加芳、江铁强 2008 物理学报 57 4649］
[16] ［16]Bai C L, Zhang X, Zhang L H 2009 Chin. Phys. B 18 475
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