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Dynamic modeling and simulation of deploying process for space solar power satellite receiver

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Abstract

To reveal some dynamic properties of the deploying process for the solar power satellite via an arbitrarily large phased array (SPS-ALPHA) solar receiver, the symplectic Runge-Kuttamethod is used to simulate the simplified model with the consideration of the Rayleigh damping effect. The system containing the Rayleigh damping can be separated and transformed into the equivalent nondamping system formally to insure the application condition of the symplectic Runge-Kutta method©First, the Lagrange equation with the Rayleigh damping governing the motion of the system is derived via the variational principle. Then, with some reasonable assumptions on the relations among the damping, mass, and stiffness matrices, the Rayleigh damping system is equivalently converted into the nondamping system formally, so that the symplectic Runge-Kutta method can be used to simulate the deploying process for the solar receiver. Finally, some numerical results of the symplectic Runge-Kutta method for the dynamic properties of the solar receiver are reported. The numerical results show that the proposed simplified model is valid for the deploying process for the SPS-ALPHA solar receiver, and the symplectic Runge-Kutta method can preserve the displacement constraints of the system well with excellent long-time numerical stability.

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References

  1. Glaser, P. Power from the Sun: its future. Science,. 162, 857–861 (1968)

    Article  Google Scholar 

  2. Hendriks, C. and Geurder, N. Solar power from space: European strategy in the light of sustainable development. European Space Agency,. 8, 1–11 (2003)

    Google Scholar 

  3. Yuka, S. Summary of studies on space solar power systems of Japan aerospace exploration agency (JAXA). Acta Astronautica,. 59, 132–138 (2006)

    Article  Google Scholar 

  4. Wang, X. D., Hu, W. P., and Deng, Z. C. Structure-preserving analysis of 2D deploying process for solar power receiver of solar power satellite (in Chinese). Journal of Dynamics and Control,. 13, 406–409 (2015)

    Google Scholar 

  5. Zhao, J., Liu, C., Tian, Q., and Hu, H. Y. Dynamic analysis of spinning deployment of a solar sail composed of viscoelastic membranes (in Chinese). Chinese Journal of Theoretical and Applied Mechanics,. 45, 746–754 (2013)

    Google Scholar 

  6. Hu, W. P., Li, Q. J., and Jiang, X. H. Coupling dynamic behaviors of spatial flexible beam with weak damping. International Journal for Numerical Methods in Engineering,. 111, 660–675 (2017)

    Article  MathSciNet  Google Scholar 

  7. Garcia-Vallejo, D., Valverde, J., and Dominguez, J. An internal damping model for the absolute nodal coordinate formulation. Nonlinear Dynamics,. 42, 347–369 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  8. Mohamed, A. A. and Shabana, A. A. A nonlinear visco-elastic constitutive model for large rotation finite element formulations. Multibody System Dynamics, 26, 57–79 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  9. Tian, Q., Zhang, Y. Q., and Chen L. P. Dynamics research on the multibody system with fractional-derivative-damper (in Chinese). Chinese Journal of Theoretical and Applied Mechanics,. 41, 920–928 (2009)

    Google Scholar 

  10. Cao, D. Z., Zhao, Z. H., and Ren, G. X. Dynamic modeling of a viscoelasticbody in a multibody system (in Chinese). Journal of Tsinghua University (Science and Technology),. 52, 483–488 (2012)

    Google Scholar 

  11. Takahashi, Y., Shimizu, N., and Suzuki, K. Introduction of damping matrix into absolute coordi- nate formulation. Asian Conference on Multibody Dynamics,. 2002, 33–40 (2002)

    Article  Google Scholar 

  12. Yoo, W. S., Lee, J. H., and Shon, J. H. Large oscillations of a thin cantilever beam: physical ex- perimental and simulation using the absolute nodal coordinate formulation. Nonlinear Dynamics,. 34, 3–29 (2003)

    Article  Google Scholar 

  13. Yoo, W. S., Lee, J. H., and Park, S. J. Large deflection analysis of a thin plate: computer simulations and experiments. Multibody System Dynamics,. 11, 185–208 (2004)

    Article  MATH  Google Scholar 

  14. Xu, B., Ou, J. P., and Jiang, J. S. Symplectic method for classical damped system response based on seperative transform (in Chinese). Journal of Mechanical Strength,. 30, 1–5 (2008)

    Google Scholar 

  15. Ying, Z. G. Advanced Dynamics-Theory and Application (in Chinese), Zhejiang University Press, Hangzhou (2011)

    Google Scholar 

  16. Feng, K. and Qin, M. Z. Symplectic Geometric Algorithms for Hamiltonian Systems (in Chinese), Zhejiang Science and Technology Press, Hangzhou (2003)

    Google Scholar 

  17. Feng, K. and Qin, M. Z. Hamiltionian algorithms for Hamiltonian dynamical systems. Progress in Nature Science,. 1, 105–116 (1991)

    Google Scholar 

  18. Feng, K. On difference schemes and symplectic geometry. Proceeding of the 1984 Beijing Sympo- sium on Differential Geometry and Differential Equations, Science Press, Beijing (1984)

    Google Scholar 

  19. Zhao, P. F. and Qin, M. Z. Multisymplectic geometry and multisymplectic Preissmann scheme for the KdV equation. Journal of Physics a General Physics,. 33, 3613–3626 (2000)

    Article  MathSciNet  MATH  Google Scholar 

  20. Zhong, W. X. Some developments of computational solid mechanics in China. Computers and Structures,. 30, 783–788 (1988)

    Article  MATH  Google Scholar 

  21. Zhong, W. X. and Williams, F. W. Precise time step integration method. Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science,. 208, 427–430 (1994)

    Google Scholar 

  22. Hairer, E., Lubich, C., and Wanner, G. Geometric Numerical Integration: Structure Preserving Algorithms for Ordinary Differential Equations, Springer-Verlag, Berlin (2002)

    Book  MATH  Google Scholar 

  23. Budd, C. J. and Piggott, M. D. Geometric integration and its applications. Handbook of Numerical Analysis, Elsevier, Amsterdam (2003)

    Book  MATH  Google Scholar 

  24. Hu, H. Y., Tian, Q., Zhang, W., and Jing, D. P. Nonlinear dynamics and control of large deployable space structures composed of trusses and meshes (in Chinese). Advances in Mechanics,. 43, 390–414 (2013)

    Google Scholar 

  25. Sheng, Y. H. Dynamics of Structures (in Chinese), Hefei University of Technology Press, Hefei (2007)

    Google Scholar 

  26. Li, Q. J., Ye, X. H., Wang, B., and Wang, Y. Nonlinear dynamic behavior of the satellite ren-dezvous and docking based on the symplectic Runge-Kutta method (in Chinese). Applied Mathe- matics and Mechanics,. 35, 1302–1304 (2014)

    Google Scholar 

  27. Jiang, C. J. On compute of parameters for 4-stage 4-order diagonally implicit symplectic Runge- Kutta methods (in Chinese). Journal of Numerical Methods and Computer Applications,. 23, 161–166 (2002)

    Google Scholar 

  28. Sanz-Serna, J. M. Runge-Kutta schemes for Hamiltonian systems. BIT Numerical Mathematics,. 28, 877–883 (1988)

    Article  MathSciNet  MATH  Google Scholar 

  29. Wu, F., Gao, Q., and Zhong, W. X. Energy and constraint preservation integration for multibody equations based on Zu Chongzhi method (in Chinese). Computer Aided Engineering,. 23, 64–68 (2014)

    Google Scholar 

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Authors and Affiliations

  1. Department of Engineering Mechanics, Northwestern Polytechnical University, Xi’an, 710072, China

    Tingting Yin, Zichen Deng, Weipeng Hu & Xindong Wang

  2. State Key Laboratory of Structural Analysis of Industrial Equipment, Dalian University of Technology, Dalian, Liaoning Province, 116023, China

    Zichen Deng & Weipeng Hu

Authors
  1. Tingting Yin
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  2. Zichen Deng
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  3. Weipeng Hu
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  4. Xindong Wang
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Corresponding author

Correspondence to Zichen Deng.

Additional information

Project supported by the National Natural Science Foundation of China (Nos. 11432010, 11672241, and 11502202) and the Open Foundation of the State Key Laboratory of Structural Analysis of Industrial Equipment of China (No.GZ1605)

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Yin, T., Deng, Z., Hu, W. et al. Dynamic modeling and simulation of deploying process for space solar power satellite receiver. Appl. Math. Mech.-Engl. Ed. 39, 261–274 (2018). https://doi.org/10.1007/s10483-018-2293-6

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  • DOI: https://doi.org/10.1007/s10483-018-2293-6

Key words

Chinese Library Classification

2010 Mathematics Subject Classification

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