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With the development of space technology, flexible appendages such as lightweight manipulators and satellite antennas, often appear in spacecrafts. Usually, the large overall motion of the flexible appendage will bring about large deformation problem. And there is a strong nonlinear coupling between the large overall motion and deformation of the flexible appendage, which brings about a large challenge to the precise control of the spacecraft. Dynamics of a rotating flexible planar beam with large deformation is investigated in this paper. A new nonlinear dynamic model of a flexible beam with large deformation is established based on an absolute node coordinate formulation (ANCF). The longitudinal and bending deformations of the flexible beam are both considered in the model. The longitudinal strain energy and bending strain energy of the beam can be calculated by using Green-Lagrangian strain tensor and the exact expression of the flexible beam curvature, respectively. A new concise expression of the bending deformation energy can be obtained by using the Lagrange identical equation. The new elastic force model is derived from the new expression of the deformation energy. The dynamic equations of the present model can precisely deal with the large deformation problem of flexible beams. Then, simulation results from three dynamic models, including the ANCF model, the high order coupling model (HOC model), and the BEAM188 model in ANSYS, are compared to prove the validity of the ANCF model proposed in this paper. And we can also find the deficiency of the HOC model from the simulation. Further study shows that the new generalized elastic force model can be simplified properly. Two simplified models are presented in this paper. The applicabilities of the simplified models are pointed out from the viewpoints of computational efficiency and accuracy. A dimensionless parameter denoted as is introduced to describe the extent to which a flexible beam pendulum undergoing free falling motion is deformed. The deformation of the flexible beam increases as increases. Considering the calculating efficiency of the dynamic model, when is small, simplified model I is chosen preferentially; when is big, simplified model Ⅱ is adopted preferentially.
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Keywords:
- absolute nodal coordinate formulation /
- large deformation /
- Green-Lagrangian strain tensor /
- Lagrange identical equation
[1] Kane T R, Ryan R R, Banerjee A K 1987 J. Guid. Control Dyn. 10 139
[2] Banerjee A K, Kane T R 1989 J. Appl. Mech. 56 887
[3] Liu J Y, Hong J Z 2004 J. Sound Vib. 278 1147
[4] Liu J Y, Li B, Hong J Z 2006 Chin. J. Theor. Appl. Mech. 38 276 (in Chinese) [刘锦阳, 李彬, 洪嘉振 2006 力学学报 38 276]
[5] Cai G P, Hong J Z Yang S X 2005 Mech. Res. Commun. 32 173
[6] He X S, Deng F Y, Wu G Y, Wang R 2010 Acta Phys. Sin. 59 25 (in Chinese) [和兴锁, 邓峰岩, 吴根勇, 王睿 2010 59 25]
[7] He X S, Li X H, Deng F Y 2011 Acta Phys. Sin. 60 024502 (in Chinese) [和兴锁, 李雪华, 邓峰岩 2011 60 024502]
[8] Chen S J, Zhang D G, Hong J Z 2013 Chin. J. Theor. Appl. Mech. 45 251 (in Chinese) [陈思佳, 章定国, 洪嘉振 2013 力学学报 45 251]
[9] Fan J H, Zhang D G 2014 Acta Phys. Sin. 63 154501 (in Chinese) [范纪华, 章定国 2014 63 154501]
[10] Simo J C, Quoc L V 1986 Comput. Methods Appl. Mech. Engineer. 58 79
[11] Qi Z H, Fang H Q, Zhang Z G, Wang L 2014 Appl. Math. Mech. 35 498 (in Chinese) [齐朝晖, 方慧青, 张志刚, 王刚 2014 应用数学和力学 35 498]
[12] Shabana A A, Hussien H A, Escalona J L 1998 J. Mech. Design 120 188
[13] Berzeri M, Shabana A A 2000 J. Sound Vib. 235 539
[14] Gerstmayr J, Irschik H 2008 J. Sound Vib. 318 461
[15] Peng L, Shabana A A 2010 Nonlinear Dyn. 61 193
[16] Tian Q, Zhang Y, Chen L, Yang J J 2010 Nonlinear Dyn. 60 489
[17] Liu C, Tian Q, Hu H Y 2012 Nonlinear Dyn. 70 1903
[18] Nachbagauer K, Gruber P, Gerstmayr J 2013 J. Computat. Nonlinear Dyn. 8 021004
[19] Shabana A A 2015 J. Computat. Nonlinear Dyn. 10 024504
[20] Chung J, Yoo H H 2002 J. Sound Vib. 249 147
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[1] Kane T R, Ryan R R, Banerjee A K 1987 J. Guid. Control Dyn. 10 139
[2] Banerjee A K, Kane T R 1989 J. Appl. Mech. 56 887
[3] Liu J Y, Hong J Z 2004 J. Sound Vib. 278 1147
[4] Liu J Y, Li B, Hong J Z 2006 Chin. J. Theor. Appl. Mech. 38 276 (in Chinese) [刘锦阳, 李彬, 洪嘉振 2006 力学学报 38 276]
[5] Cai G P, Hong J Z Yang S X 2005 Mech. Res. Commun. 32 173
[6] He X S, Deng F Y, Wu G Y, Wang R 2010 Acta Phys. Sin. 59 25 (in Chinese) [和兴锁, 邓峰岩, 吴根勇, 王睿 2010 59 25]
[7] He X S, Li X H, Deng F Y 2011 Acta Phys. Sin. 60 024502 (in Chinese) [和兴锁, 李雪华, 邓峰岩 2011 60 024502]
[8] Chen S J, Zhang D G, Hong J Z 2013 Chin. J. Theor. Appl. Mech. 45 251 (in Chinese) [陈思佳, 章定国, 洪嘉振 2013 力学学报 45 251]
[9] Fan J H, Zhang D G 2014 Acta Phys. Sin. 63 154501 (in Chinese) [范纪华, 章定国 2014 63 154501]
[10] Simo J C, Quoc L V 1986 Comput. Methods Appl. Mech. Engineer. 58 79
[11] Qi Z H, Fang H Q, Zhang Z G, Wang L 2014 Appl. Math. Mech. 35 498 (in Chinese) [齐朝晖, 方慧青, 张志刚, 王刚 2014 应用数学和力学 35 498]
[12] Shabana A A, Hussien H A, Escalona J L 1998 J. Mech. Design 120 188
[13] Berzeri M, Shabana A A 2000 J. Sound Vib. 235 539
[14] Gerstmayr J, Irschik H 2008 J. Sound Vib. 318 461
[15] Peng L, Shabana A A 2010 Nonlinear Dyn. 61 193
[16] Tian Q, Zhang Y, Chen L, Yang J J 2010 Nonlinear Dyn. 60 489
[17] Liu C, Tian Q, Hu H Y 2012 Nonlinear Dyn. 70 1903
[18] Nachbagauer K, Gruber P, Gerstmayr J 2013 J. Computat. Nonlinear Dyn. 8 021004
[19] Shabana A A 2015 J. Computat. Nonlinear Dyn. 10 024504
[20] Chung J, Yoo H H 2002 J. Sound Vib. 249 147
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