Nonlinear Dynamics

, Volume 94, Issue 4, pp 2863–2877 | Cite as

Nonlinear vibration phenomenon of maneuvering spacecraft with flexible jointed appendages

  • Jin Wei
  • Dengqing CaoEmail author
  • Hua Huang
Original Paper


A nonlinear analytical model for a spacecraft with flexible jointed appendages is presented and subsequently used to investigate the nonlinear vibration phenomenon of the system caused by the joints nonlinearities during the spacecraft maneuvering. In this model, the joint transmitted characteristics which included linear and nonlinear stiffness, damping and friction are introduced into the system by applying the equilibrium conditions between the beams and the joints. Consequently, an explicit set of reduced-order nonlinear ordinary differential equations (ODEs) of motion for the flexible spacecraft with nonlinear joints are obtained based on the global mode method. Through the nonlinear ODEs obtained in this model, the dynamic responses of the system with various joint parameters are worked out numerically for the cases of attitude maneuver and orbit maneuver, respectively. For the case of attitude maneuver, the simulation results show that the damping and friction in the joints have a great influence on the vibration response of the system, especially the residual vibration. For the case of orbit maneuver, some nonlinear behaviors caused by the nonlinear joints are observed such as hardening, jump, sub-harmonic and super-harmonic resonance. More importantly, due to the cubic stiffness of the joint, modal coupling is exhibited, which result in the interaction between translation and rotation of the central rigid body.


Flexible spacecraft Nonlinear joints Nonlinear dynamic model Modal coupling Nonlinear vibration 



This work was supported by the National Natural Science Foundation of China under Grant Nos. 11732005 and 11472089.

Compliance with ethical standards

Conflict of interest

The authors declare that they have no conflict of interest.


  1. 1.
    Wang, J.H., Liou, C.M.: Experimental identification of mechanical joint parameters. J. Vib. Acoust. 113(1), 28–36 (1991)CrossRefGoogle Scholar
  2. 2.
    Ren, Y., Lim, T.M., Lim, M.K.: Identification of properties of nonlinear joints using dynamic test data. J. Vib. Acoust. 120(2), 324–330 (1998)CrossRefGoogle Scholar
  3. 3.
    Ahmadian, H., Jalali, H.: Identification of bolted lap joints parameters in assembled structures. Mech. Syst. Signal Process. 21(2), 1041–1050 (2007)CrossRefGoogle Scholar
  4. 4.
    Crawley, E.F., Aubert, A.C.: Identification of nonlinear structural elements by force-state mapping. AIAA J. 24(1), 155–162 (1986)CrossRefGoogle Scholar
  5. 5.
    Crawley, E.F., O’Donnell, K.J.: Force-state mapping identification of nonlinear joints. AIAA J. 25(7), 1003–1010 (1987)CrossRefGoogle Scholar
  6. 6.
    Wang, J.H., Huang, H.Y.: Model and parameters identification of non-linear joint by force-state mapping in frequency domain. J. Mech. 23(4), 367–380 (2007)CrossRefGoogle Scholar
  7. 7.
    Jalali, H., Ahmadian, H., Mottershead, J.E.: Identification of nonlinear bolted lap-joint parameters by force-state mapping. Int. J. Solids Struct. 44(25), 8087–8105 (2007)CrossRefGoogle Scholar
  8. 8.
    Wu, S., Zhao, S., Wu, D., Luo, M.: Parameter identification of nonlinear joints in spacecraft by force-state mapping. J. Harbin Eng. Univ. 36(12), 1578–1583 (2015)zbMATHGoogle Scholar
  9. 9.
    Kim, W.-J., Lee, B.-Y., Park, Y.-S.: Non-linear joint parameter identification using the frequency response function of the linear substructure. In: ARCHIVE Proceedings of the Institution of Mechanical Engineers Part C Journal of Mechanical Engineering Science 1989–1996 (vols. 203–210), vol. 218, number 9, pp. 947–955 (2004)Google Scholar
  10. 10.
    Ratcliffe, M.J., Lieven, N.A.J.: A generic element-based method for joint identification. Mech. Syst. Signal Process. 14(1), 3–28 (2000)CrossRefGoogle Scholar
  11. 11.
    Hsu, S.T., Griffin, J.H., Bielak, J.: How gravity and joint scaling affect dynamics response. AIAA J. 27(9), 1280–1287 (1989)CrossRefGoogle Scholar
  12. 12.
    Folkman, S.L., Redd, F.J.: Gravity effects on damping of a space structure with pinned joints. J. Guid. Control Dyn. 13(2), 228–233 (1990)CrossRefGoogle Scholar
  13. 13.
    Folkman, S.L., Rowsell, E.A., Ferney, G.D.: Influence of pinned joints on damping and dynamic behavior of a truss. J. Guid. Control Dyn. 18(6), 1398–1403 (1995)CrossRefGoogle Scholar
  14. 14.
    Dutson, J.D., Folkman, S.L.: A nonlinear finite element model of a truss using pinned joints. In: Structure, Structural Dynamics and Materials Conference, Salt Lake City 1996. AIAA Meeting Papers on Disc, pp. 793–803Google Scholar
  15. 15.
    Moon, F.C., Li, G.X.: Experimental study of chaotic vibrations in a pin-jointed space truss structure. AIAA J. 28(5), 915–921 (1990)CrossRefGoogle Scholar
  16. 16.
    Onoda, J., Sano, T., Minesugi, K.: Passive damping of truss vibration using preloaded joint backlash. AIAA J. 33(7), 1335–1341 (1995)CrossRefGoogle Scholar
  17. 17.
    Bowden, M., Dugundji, J.: Joint damping and nonlinearity in dynamics of space structures. AIAA J. 28(4), 740–749 (2012)CrossRefGoogle Scholar
  18. 18.
    Zhang, J., Guo, H.W., Liu, R.Q., Wu, J., Kou, Z.M., Deng, Z.Q.: Nonlinear dynamic characteristic analysis of jointed beam with clearance. Acta Astronaut. 129, 135–146 (2016)CrossRefGoogle Scholar
  19. 19.
    Shi, G., Atluri, S.N.: Nonlinear dynamic response of frame-type structures with hysteretic damping at the joints. AIAA J. 30(1), 234–240 (1992)CrossRefGoogle Scholar
  20. 20.
    Ferri, A.A., Heck, B.S.: Analytical investigation of damping enhancement using active and passive structural joints. J. Guid. Control Dyn. 15(5), 1258–1264 (1992)CrossRefGoogle Scholar
  21. 21.
    Yoshida, T.: Dynamic characteristic formulations for jointed space structures. J. Spacecr. Rockets 43(4), 771–779 (2006)CrossRefGoogle Scholar
  22. 22.
    Bingham, J.G., Folkman, S.L.: Measured influence of gravity on the dynamic behavior of a truss using pinned joints. In: Structure, Structural Dynamics and Materials Conference, Salt Lake City 1996. AIAA Meeting Papers on Disc, pp. 1043–1053Google Scholar
  23. 23.
    Wei, J., Cao, D., Wang, L., Huang, H., Huang, W.: Dynamic modeling and simulation for flexible spacecraft with flexible jointed solar panels. Int. J. Mech. Sci. 130, 558–570 (2017)CrossRefGoogle Scholar
  24. 24.
    Clough, R.W., Penzien, J.: Dynamics of Structures, 3rd edn. Computers & Structures, Inc, Berkeley (2003)zbMATHGoogle Scholar

Copyright information

© Springer Nature B.V. 2018

Authors and Affiliations

  1. 1.School of AstronauticsHarbin Institute of TechnologyHarbinChina
  2. 2.China Academy of Space TechnologyBeijingChina

Personalised recommendations