Abstract
The nonlinear dynamic control equation of a flexible multi-body system with definite moving attitude is discussed. The motion of the aircraft in space is regarded as known and the influence of the flexible structural members in the aircraft on the motion and attitude of the aircraft is analyzed. By means of a hypothetical mode, the deformation of flexible members is regarded as composed of the line element vibration in the axial direction of rectangular coordinates in space. According to Kane’ s method in dynamics, a dynamic equation is established, which contains the structural stiffness matrix that represents the elastic deformation and the geometric stiffness matrix that represents the nonlinear deformation of the deformed body. Through simplification the dynamic equation of the influence of the planar flexible body with a windsurfboard structure on the spacecraft motion is obtained. The numerical solution for this kind of equation can be realized by a computer.
Similar content being viewed by others
References
Banerjee A K, Kane T R. Dynamics of a plate in large overall motion [J]. ASME J of Applied Mech, 1989, 56(1): 887–892.
Kane T R, Ryan R R, Banerjee A K. Dynamics of a cantilever beam attached to a moving base[J]. J of Guidance, Control and Dynamics, 1987, 10(2): 135–151.
Kane T R, Ryan R R, Banerjee A K. Reply by authors to K W London [J]. J of Guidance, Control and Dynamics, 1989, 12(2):286–287.
Levinson D A, Kane T R. Autolev—a New Approach to Multibody Dynamics [M]. Schiehlen W (ed). Mutlibody Systems Handbook. Springer-Verlag, Berlin, 1990, 81–102.
Roberson K E, Schwertassek K. Dynamics of Multi-body System[M]. Springer-Verlag, New York, 1998, 122–156.
Rosenthal K E, Shermand M A. High performance multi-body simulations via symbolic equation manipulation and Kane’s method [J]. J of the Astronautical Sci, 1986, 34(3):223–239.
Likins P W. Geometric stiffness characteristics of a rotating elastic appendage[J]. International J Solid and Structures, 1974, 10(2):161–167.
Wu S C, Haug E J. Geometric nonlinear substructuring for dynamics of flexibly mechanical system[J]. J for Numerical Method in Engineering, 1989, 44(3):135–146.
Zeiler T Buttrill C. Dynamics analysis of an unrestrained rotating structure through nonlinear simulation[C]. AIAA 29th Structure Structural Dynamics and Materials Conference. Williamsburg, Va., 1988, 18–20.
Banerjee A K, Dickens J M. Dynamics of an arbitrary flexibly body in large rotation .and .translation[J]. ASME J of Mech,1990, 13(2):221–227.
Banerjee A K, Lemak M E. Multi-flexibly dynamics capturing motion induced stiffness[J]. Transaction of the ASME, 1991, 58(4):113–121.
Yang Yuanming, Guo Jiansheng. Dynamics modeling of the flexibly body with determined movement position[J]. J of Huazhong University of Sci and Tech, 1999, 19(7):103–105.
Yang Yuanming, Zhang Wei. Dynamics modeling of the flexibly multi-body[J]. Acta Mechanica Solid Sinica, 1999, 20: 153–158.
Kane T R, Likins P W, Levinson D A. Spacecraft Dynamics[M]. McGraw-Hill, New York, 1983,247.
Author information
Authors and Affiliations
Corresponding author
Additional information
Project supported by the Natural Science Foundation of Henan Province (No.0311011100)
Rights and permissions
About this article
Cite this article
Yang, Ym., Zhang, W., Song, Tx. et al. Dynamic analysis of flexible body with definite moving attitute. Appl Math Mech 27, 133–140 (2006). https://doi.org/10.1007/s10483-006-0117-1
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/s10483-006-0117-1