0
Research Papers

Dynamics of a Deployable Mesh Reflector of Satellite Antenna: Form-Finding and Modal Analysis

[+] Author and Article Information
Pei Li

MOE Key Laboratory of Dynamics and
Control of Flight Vehicle,
School of Aerospace Engineering,
Beijing Institute of Technology,
Beijing 100081, China
e-mail: lipei0603@sina.com

Cheng Liu

MOE Key Laboratory of Dynamics and
Control of Flight Vehicle,
School of Aerospace Engineering,
Beijing Institute of Technology,
Beijing 100081, China;
MIIT Key Laboratory of Autonomous Navigation
and Control for Deep Space Exploration,
School of Aerospace Engineering,
Beijing Institute of Technology,
Beijing 100081, China
e-mail: liucheng_bit@aliyun.com

Qiang Tian

MOE Key Laboratory of Dynamics and
Control of Flight Vehicle,
School of Aerospace Engineering,
Beijing Institute of Technology,
Beijing 100081, China;
MIIT Key Laboratory of Autonomous Navigation
and Control for Deep Space Exploration,
School of Aerospace Engineering,
Beijing Institute of Technology,
Beijing 100081, China
e-mail: tianqiang_hust@aliyun.com

Haiyan Hu

MOE Key Laboratory of Dynamics and
Control of Flight Vehicle,
School of Aerospace Engineering,
Beijing Institute of Technology,
Beijing 100081, China;
MIIT Key Laboratory of Autonomous Navigation
and Control for Deep Space Exploration,
School of Aerospace Engineering,
Beijing Institute of Technology,
Beijing 100081, China
e-mail: haiyan_hu@bit.edu.cn

Yanping Song

Xi'an Institute of Space Radio Technology, Xi'an,
Shaanxi 71000, China

1Corresponding author.

Contributed by the Design Engineering Division of ASME for publication in the JOURNAL OF COMPUTATIONAL AND NONLINEAR DYNAMICS. Manuscript received April 29, 2015; final manuscript received April 8, 2016; published online May 12, 2016. Assoc. Editor: Paramsothy Jayakumar.

J. Comput. Nonlinear Dynam 11(4), 041017 (May 12, 2016) (12 pages) Paper No: CND-15-1115; doi: 10.1115/1.4033440 History: Received April 29, 2015; Revised April 08, 2016

Mesh reflectors with large apertures have been used in many communication satellites. The performance of antenna reflectors crucially depends on the faceting error of the reflective surface, which is approximated by using meshes. The force density method (FDM) has been widely used for the form-finding analysis of mesh reflectors. However, after performing form-finding of some meshes, the effective reflective area will decrease. In addition, the form-finding of the auxiliary mesh has received little attention, and it cannot be achieved by using the FDM. Thus, in this study, an effective form-finding methodology that combines the iterative FDM and the minimum norm method (MNM) is proposed. To consider the flexibility of the reflector ring truss, a static analysis of the ring truss under the tension force actions is also performed in the form-finding processes. The reflector flexible parts are described by the absolute nodal coordinate formulation (ANCF). Finally, the form-finding analysis of the reflector with the standard configuration, the central hub configuration, and the circular configuration is performed to validate the proposed methodology. The influence of the mesh tension force on the reflector natural frequencies is also studied. After performing the form-finding analysis, the initial configuration of the reflector with tensioned meshes for the deployment dynamics study can be determined. Based on this paper, the deployment dynamics of a complex AstroMesh reflector will be studied in a successive paper “Dynamics of a Deployable Mesh Reflector of Satellite Antenna: Parallel Computation and Deployment Simulation.”

Copyright © 2016 by ASME
Your Session has timed out. Please sign back in to continue.

References

Tibert, A. G. , 2002, “ Deployable Tensegrity Structure for Space Applications,” Ph.D. dissertation, Royal Institute of Technology, Stockholm, Sweden.
Thomson, M. W. , 1999, “ The Astromesh Deployable Reflector,” IEEE Trans. Antennas Propag., 3, pp. 1516–1535.
Meguro, A. , Harada, S. , and Watanabe, M. , 2003, “ Key Technologies for High-Accuracy Large Mesh Antenna Reflectors,” Acta Astronaut., 53(11), pp. 899–908. [CrossRef]
You, Z. , and Pellegrino, S. , 1996, “ Cable-Stiffened Pantographic Deployable Structures Part 2: Mesh Reflector,” AIAA J., 35(8), pp. 1348–1355. [CrossRef]
Thomson, M. W. , Marks, G. W. , and Hedgepeth, J. M. , 1997, “ Light-Weight Reflector for Concentrating Radiation,” U.S. Patent No. 5,680,145.
Hedgepeth, J. M. , 1982, “ Influence of Fabrication Tolerances on the Surface Accuracy of Large Antenna Structures,” AIAA J., 20(5), pp. 680–686. [CrossRef]
Northrop Grumman, “AstroMesh Reflector Family,” Northrop Grumman Corp., Falls Church, VA.
Ma, X. F. , Song, Y. P. , Li, Z. J. , Li, T. J. , Wang, Z. W. , and Deng, H. Q. , 2013, “ Mesh Reflector Antennas: Form-Finding Analysis Review,” AIAA Paper No. 2013-1576.
Wang, Z. W. , Li, T. J. , and Cao, Y. Y. , 2013, “ Active Shape Adjustment of Cable Net Structures With PZT Actuators,” Aerosp. Sci. Technol., 26(1), pp. 160–168. [CrossRef]
Tibert, A. G. , and Pellegrino, S. , 2003, “ Review of Form-Finding Methods for Tensegrity Structures,” Int. J. Solids Struct., 18(4), pp. 209–223. [CrossRef]
Li, T. J. , Guo, J. , and Cao, Y. Y. , 2011, “ Dynamic Characteristics Analysis of Deployable Space Structures Considering Joint Clearance,” Acta Astronaut., 68(7–8), pp. 974–983. [CrossRef]
Tran, H. C. , and Lee, J. , 2010, “ Advanced Form-Finding of Tensegrity Structures,” Comput. Struct., 88(3–4), pp. 237–246. [CrossRef]
Tran, H. C. , and Lee, J. , 2010, “ Initial Self-Stress Design of Tensegrity Grid Structures,” Comput. Struct., 88(9–10), pp. 558–566. [CrossRef]
Linkwitz, K. , 1999, “ Form-Finding by the ‘Direct Approach’ and Pertinent Strategies for the Conceptual Design of Prestressed and Hanging Structures,” Int. J. Space Struct., 14(2), pp. 73–87. [CrossRef]
Linkwitz, K. , and Schek, H. J. , 1971, “ Remarks Concerning the Analysis of Prestressed Cable Structures,” Ing.-Arch., 40(3), pp. 145–158. [CrossRef]
Tibert, A. G. , 2003, “ Optimal Design of Tension Truss Antennas,” AIAA Paper No. 2003-1629.
Tanaka, H. , Shimozono, N. , and Natori, M. C. , 2008, “ A Design Method for Cable Network Structures Considering the Flexibility of Supporting Structures,” Trans. Jpn. Soc. Aeronaut. Space Sci., 50(170), pp. 267–273. [CrossRef]
Tanaka, H. , and Natori, M. C. , 2006, “ Shape Control of Cable Net Structures Based on Concept of Self-Equilibrated Stresses,” JSME Int. J. Ser. C: Mech. Syst. Mach. Elem. Manuf., 49(4), pp. 1067–1072. [CrossRef]
Tanaka, H. , and Natori, M. C. , 2004, “ Shape Control of Space Antennas Consisting of Cable Networks,” Acta Astronaut., 55(3–9), pp. 519–527. [CrossRef]
Morterolle, S. , Maurin, B. , Quirant, J. , and Dupuy, C. , 2012, “ Numerical Form-Finding of Geotensoid Tension Truss for Mesh Reflector,” Acta Astronaut., 76, pp. 154–163. [CrossRef]
Li, T. J. , Zhou, M. H. , and Duan, B. Y. , 2008, “ A Method of Form-Finding Analysis for Flexible Cable Net Structures of Deployable Antennas,” J. Astronaut., 29, pp. 794–798.
Yang, D. W. , 2010, “ Structure Design and Profile Adjustment of Large Deployable Mesh Antenna for Satellite,” Ph.D. dissertation, Xidian University, Xi'an, China.
Shabana, A. A. , 1996, “ An Absolute Nodal Coordinates Formulation for the Large Rotation and Deformation Analysis of Flexible Bodies,” University of Illinois at Chicago, Chicago, IL, Technical Report No. MBS96-1-UIC.
Eberhard, P. , and Schiehlen, W. , 2006, “ Computational Dynamics of Multibody Systems History, Formalisms, and Applications,” ASME J. Comput. Nonlinear Dyn., 1(1), pp. 3–12. [CrossRef]
Schiehlen, W. , 2007, “ Research Trends in Multibody System Dynamics,” Multibody Syst. Dyn., 18(1), pp. 3–13. [CrossRef]
Gerstmayr, J. , and Shabana, A. A. , 2006, “ Analysis of Thin Beams and Cables Using the Absolute Nodal Coordinate Formulation,” Nonlinear Dyn., 45, pp. 109–130. [CrossRef]
Shabana, A. A. , and Mikkola, A. M. , 2003, “ Use of the Finite Element Absolute Nodal Coordinate Formulation in Modeling Slope Discontinuity,” ASME J. Mech. Des., 125(2), pp. 342–350. [CrossRef]
Tian, Q. , Chen, L. , Zhang, Y. , and Yang, J. , 2009, “ An Efficient Hybrid Method for Multibody Dynamics Simulation Based on Absolute Nodal Coordinate Formulation,” ASME J. Comput. Nonlinear Dyn., 4(2), p. 021009. [CrossRef]
Liu, C. , Tian, Q. , and Hu, H. Y. , 2013, “ Dynamic Analysis of Membrane Systems Undergoing Overall Motions, Large Deformations and Wrinkles Via Thin Shell Elements of ANCF,” Comput. Methods Appl. Mech. Eng., 258, pp. 81–95. [CrossRef]
Lai, C. Y. , and Pellegrino, S. , 1999, “ Shape and Stress Analysis of Offset CRTS Reflectors,” Department of Engineering, University of Cambridge, Cambridge, UK, Report No. CUED/D-STRUCT/TR177.
Pontoppidan, K. , 1984, “ Electrical Consequences of Mechanical Antenna Characteristics,” ESA Workshop on Mechanical Technology for Antennas, pp. 41–47.
Penrose, R. A. , 1955, “ A Generalized Inverse for Matrices,” Proc. Cambridge Philos. Soc., 51(3), pp. 406–413. [CrossRef]
Al-Sumait, J. S. , AL-Othman, A. K. , and Sykulski, J. K. , 2007, “ Application of Pattern Search Method to Power System Valve-Point Economic Load Dispatch,” Int. J. Electr. Power Energy Syst., 29(10), pp. 720–730. [CrossRef]
Liu, C. , Tian, Q. , and Hu, H. Y. , 2012, “ New Spatial Curved Beam and Cylindrical Shell Elements of Gradient-Deficient Absolute Nodal Coordinate Formulation,” Nonlinear Dyn., 70(3), pp. 1903–1918. [CrossRef]
Shabana, A. A. , 2008, Computational Continuum Mechanics, Cambridge University Press, Cambridge, UK.
Shabana, A. A. , and Yakoub, R. Y. , 2001, “ Three-Dimensional Absolute Nodal Coordinate Formulation for Beam Elements: Theory,” ASME J. Mech. Des., 123(4), pp. 606–613. [CrossRef]
Shabana, A. A. , and Maqueda, L. G. , 2008, “ Slope Discontinuities in the Finite Element Absolute Nodal Coordinate Formulation: Gradient Deficient Elements,” Multibody Syst. Dyn., 20(3), pp. 239–249. [CrossRef]

Figures

Grahic Jump Location
Fig. 1

AstroMesh paraboloid reflector and its meshes

Grahic Jump Location
Fig. 2

The offset parabolic surface with standard configuration: (a) axonometric view and (b) view projected onto X1Z1-plane

Grahic Jump Location
Fig. 3

The offset parabolic surface with circular configuration: (a) axonometric view and (b) view projected onto X1Z1-plane

Grahic Jump Location
Fig. 4

The least squares paraboloid and the mesh triangular facet

Grahic Jump Location
Fig. 5

Configuration changes of the AM0 and AM3 meshes before and after form-finding analysis: (a) AM0 mesh and (b) AM3 mesh

Grahic Jump Location
Fig. 6

Configuration changes for the AM3 meshes before and after form-finding analysis

Grahic Jump Location
Fig. 7

A slope deficient ANCF beam element

Grahic Jump Location
Fig. 8

A part of the finite element model of the ring truss meshed by using the fully parameterized beam element of ANCF

Grahic Jump Location
Fig. 9

The reflector form-finding computation flowchart

Grahic Jump Location
Fig. 10

The initial configuration of the ring truss: (a) view projected onto X1Z1-plane and (b) axonometric view

Grahic Jump Location
Fig. 11

The scaled deformation configurations of the ring truss under external forces: (a) standard configuration, (b) central hub configuration, and (c) circular configuration

Grahic Jump Location
Fig. 12

The maximum tension ratio of the inner cables of the front net

Grahic Jump Location
Fig. 13

Configuration changes for the AM3 mesh before and after form-finding analysis (in XY-plane)

Grahic Jump Location
Fig. 14

The Cauchy's stresses along the cable axis of the cables in the front (a) and the rear (b) meshes after form-finding

Grahic Jump Location
Fig. 15

The lowest three mode shapes of the 30 m circular antenna: (a) the first mode shape (0.1119 Hz), (b) the second mode shape (0.2746 Hz), and (c) the third mode shape (1.3604 Hz)

Tables

Errata

Discussions

Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In