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Studies on global analytical mode for a three-axis attitude stabilized spacecraft by using the Rayleigh–Ritz method

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Abstract

With extending the Rayleigh–Ritz procedure to study the hub-plate system, the characteristics of global analytical modes are addressed for a typical rigid–flexible coupling dynamic system, i.e., a three-axis attitude stabilized spacecraft installed with a pair of solar arrays. The displacement field of the solar arrays is expressed as a series of admissible functions which is a set of characteristic orthogonal polynomials generated directly by employing Gram–Schmidt process. The rigid body motion of spacecraft is represented by the product of constant and generalized coordinate. Then, through Rayleigh–Ritz procedure, the eigenvalue equation of the three-axis attitude stabilized spacecraft installed with a pair of solar arrays is derived. Solving this eigenvalue equation, the frequencies and analytical expressions of global modes for the flexible spacecraft are obtained. To validate the present analysis, comparisons between the results of the present method and ANSYS software are performed and very good agreement is achieved. The convergence studies demonstrate the high accuracy, excellent convergence and high efficiency of the present approach. Finally, the method is applied to study the characteristics of global modes of the flexible spacecraft.

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Acknowledgments

This research has been supported by the National Natural Science Foundation of China (Grant No. 11472089).

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Authors and Affiliations

  1. School of Astronautics, Harbin Institute of Technology, PO Box 137, Harbin, 150001, People’s Republic of China

    Lun Liu, Dengqing Cao & Xiaojun Tan

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  1. Lun Liu
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  2. Dengqing Cao
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Correspondence to Dengqing Cao.

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Liu, L., Cao, D. & Tan, X. Studies on global analytical mode for a three-axis attitude stabilized spacecraft by using the Rayleigh–Ritz method. Arch Appl Mech 86, 1927–1946 (2016). https://doi.org/10.1007/s00419-016-1155-3

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  • DOI: https://doi.org/10.1007/s00419-016-1155-3

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