环形桁架结构模态实验及有限元仿真分析
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摘要
针对大型可展开环形桁架天线结构开展了模态实验和有限元仿真分析。首先设计加工了环形桁架实验模型,采用锤击法对自由边界条件下环形桁架结构进行了实验模态分析,得到环形桁架结构的前六阶固有频率及其对应模态振型,并通过模态置信准则对实验结果进行了可靠性分析。其次,建立了环形桁架实验模型的有限元模型并进行模态分析,仿真得到其前六阶固有频率和模态振型。最后详细对比分析了实验结果与有限元仿真结果。结果表明:二者固有频率误差小于5%,且实验模态振型与有限元仿真模态振型一致,证明了本文分析结果真实可靠;同时,分析得到了环形桁架结构第一、二阶振型为椭圆形,第三、四阶振型为三角形,第五、六阶振型为四边形。
In this paper, the modal experiment analysis and FEM(finite element method) simulation of a ring truss structure which modeled a large deployable antenna are carried out. First, an experimental model for the large deployable antenna astromesh is designed and manufactured. And the experimental modal analysis of the ring truss under the free boundary condition is conducted by using hammer method. Based on the experiment results, the first six order natural frequencies, and the first six order mode shapes are obtained. And the MAC(Modal Assurance Criterion) is introduced to verify this experimental results. Secondly, modal analysis of the ring truss structure under the free boundary condition is conducted by using FEM. The first six order natural frequencies and corresponding damping ratio and the first six order mode shapes are also obtained. Finally, the results between the experiment method and FEM are compared. It is found that the error for the natural frequencies is acceptable while the mode shapes show very good agreement. In summary, the results of the different methods have good consistency, which can confirms that the analysis of this paper is feasible and reliable. Meanwhile, the natural frequency and mode shape of each order are obtained.
In this paper, the modal experiment analysis and FEM(finite element method) simulation of a ring truss structure which modeled a large deployable antenna are carried out. First, an experimental model for the large deployable antenna astromesh is designed and manufactured. And the experimental modal analysis of the ring truss under the free boundary condition is conducted by using hammer method. Based on the experiment results, the first six order natural frequencies, and the first six order mode shapes are obtained. And the MAC(Modal Assurance Criterion) is introduced to verify this experimental results. Secondly, modal analysis of the ring truss structure under the free boundary condition is conducted by using FEM. The first six order natural frequencies and corresponding damping ratio and the first six order mode shapes are also obtained. Finally, the results between the experiment method and FEM are compared. It is found that the error for the natural frequencies is acceptable while the mode shapes show very good agreement. In summary, the results of the different methods have good consistency, which can confirms that the analysis of this paper is feasible and reliable. Meanwhile, the natural frequency and mode shape of each order are obtained.
引文
[1]Li Tuanjie.Deployment analysis and control of deployable space antenna[J].Aerospace Science and Technology,2012,18:42-47.
[2]Thomson M W.The astromesh deployable reflector[C]//Antennas and Propagation Society International Symposium.Carpinteria,CA:IEEE,1999:1516-1519.
[3]胡海岩,田强,张伟,等.大型网架式可展开空间结构的非线性动力学与控制[J].力学进展,2013,43(4):390-414.(Hu Haiyan,Tian Qiang,Zhang Wei,et al.Nonlinear dynamics and control of large deployable space structures composed of trusses and meshes[J].Advances in Mechanics,2013,43(4):390-414(in Chinese)).
[4]刘荣强,田大可,邓宗全.空间可展开天线结构的研究现状与展望[J].机械设计,2010,27(9):1-7.(Liu Rongqiang,Tian Dake,Deng Zongquan.Research status and prospect of deployable antenna structure in space[J].Machine Design,2010,27(9):1-7(in Chinese)).
[5]Takano T,Miura K,Natori M,et al.Deployable antenna with 10m maximum diameter for space use[J].IEEE Transactionson Antenna Sand Propagation,2004,52(1):2-11.
[6]Thomson M W.Astromesh deployable reflectors for kuand kaband commercial satellites[C]//20th AIAA International Communication Satellite Systems Conference and Exhibit.Montreal,Canada:AIAA,2002:2002-2032.
[7]Tibert A G.Optimal design of tension truss antennas[C]//44th AIAA/ASME/ASCE/AHS Structures,Structural Dynamics,and Materials Conference.Norfolk,Virginia:AIAA,2003:2051-2060.
[8]Mehran M.Methods of analyzing surface accuracy of large antenna structures duo to manufacturing tolerances[C]//44th AIAA/ASME/ASCE/AHS Structures,Structural Dynamics,and Materials Conference.Norfolk,Virginia:AIAA,2003:508-517.
[9]Wilson W J,Njoku E G,Yueh S H.Active/passive microwave system with deployable mesh antenna for space borne ocean salinity measurements[R].[S.l.]:International Geosciences and Remote Sensing Symposium,2000(6):2549-2551.
[10]Smith T,Lee B,Semler D,et al.A large S-band antenna for a mobile satellite[C]//Space 2004 Conference and Exhibit.San Diego,Califorhia:AIAA,2004:2317-2324.
[11]Duan Baoyan,Luo Ying.On optimization of large cablemesh surface antenna with both deployed and retracted states[R].[S.l.]:11th AIAA/ISSMO Multidisciplinary Analysis and Optimization Conference,2006:943-950.
[12]陶成,刘丽坤,周志成,等.环形桁架式天线展开不同步现象分析[J].中国空间科学技术,2015,35(1):1-8.(Tao Cheng,Liu Likun,Zhou Zhicheng,et al.Analysis of the non-synchronous phenomenon of circular truss antenna[J].Space Science and Technology in China,2015,1:1-8(in Chinese)).
[13]赵孟良.空间可展结构展开过程动力学理论分析、仿真及试验[D].杭州:浙江大学,2007:29-32.(Zhao Mengliang.Theoretical analysis,simulation and experiment of the dynamic process of deployable space deployable structure[D].Hangzhou:Zhejiang University,2007:29-32(in Chinese)).
[14]韦娟芳,赵人杰,关富玲.星载天线结构的发展趋势[J].空间电子技术,2002(1):49-54.(Wei Juanfang,Zhao Renjie,Guan Fuling.Development trend of satellite antenna structure[J].Space Electronic Technology,2002(1):49-54(in Chinese)).
[15]李团结,张琰,李涛.周边桁架可展天线展开过程动力学分析及控制[J].航空学报,2009,30(3):444-449.(Li Tuanjie,Zhang Yan,Li Tao.Dynamic analysis and control of deployable antenna deployable process[J].Aeronautical Journal,2009,30(3):444-449(in Chinese)).
[16]罗鹰,段宝岩.周边桁架式展开天线几何布局优化[J].空间科学学报,2004,24(2):132-137.(Luo Ying,Duan Baoyan.Geometric layout optimization of perimeter truss deployable antenna[J].Journal of Space Science,2004,24(2):132-137(in Chinese)).
[17]李刚,关富玲.环形桁架展开天线索网的预拉力优化技术及工程应用[J].固体力学学报,2006(增刊1):180-185.(Li Gang,Guan Fuling.Optimization of pretension in net of astromesh deployable reflector and engineering application[J].Acta Mechanica Solida Sinica,2006(S1):180-185(in Chinese)).
[18]曹树谦,张文德.振动结构模态分析:理论、实验与应用[M].天津:天津大学出版社,2001.(Cao Shuqian,Zhang Wende.Modal analysis of vibration structure:theory,experiment and application[M].Tianjin:Tianjin University Press,2001(in Chinese)).
[19]田大可.模块化空间可展开天线支撑桁架设计与实验研究[D].哈尔滨:哈尔滨工业大学,2011:29-32.(Tian Dake.Design and experimental research on truss structure for modular space deployable antenna[D].Harbin:Harbin Institute of University,2011:29-32(in Chinese)).
[2]Thomson M W.The astromesh deployable reflector[C]//Antennas and Propagation Society International Symposium.Carpinteria,CA:IEEE,1999:1516-1519.
[3]胡海岩,田强,张伟,等.大型网架式可展开空间结构的非线性动力学与控制[J].力学进展,2013,43(4):390-414.(Hu Haiyan,Tian Qiang,Zhang Wei,et al.Nonlinear dynamics and control of large deployable space structures composed of trusses and meshes[J].Advances in Mechanics,2013,43(4):390-414(in Chinese)).
[4]刘荣强,田大可,邓宗全.空间可展开天线结构的研究现状与展望[J].机械设计,2010,27(9):1-7.(Liu Rongqiang,Tian Dake,Deng Zongquan.Research status and prospect of deployable antenna structure in space[J].Machine Design,2010,27(9):1-7(in Chinese)).
[5]Takano T,Miura K,Natori M,et al.Deployable antenna with 10m maximum diameter for space use[J].IEEE Transactionson Antenna Sand Propagation,2004,52(1):2-11.
[6]Thomson M W.Astromesh deployable reflectors for kuand kaband commercial satellites[C]//20th AIAA International Communication Satellite Systems Conference and Exhibit.Montreal,Canada:AIAA,2002:2002-2032.
[7]Tibert A G.Optimal design of tension truss antennas[C]//44th AIAA/ASME/ASCE/AHS Structures,Structural Dynamics,and Materials Conference.Norfolk,Virginia:AIAA,2003:2051-2060.
[8]Mehran M.Methods of analyzing surface accuracy of large antenna structures duo to manufacturing tolerances[C]//44th AIAA/ASME/ASCE/AHS Structures,Structural Dynamics,and Materials Conference.Norfolk,Virginia:AIAA,2003:508-517.
[9]Wilson W J,Njoku E G,Yueh S H.Active/passive microwave system with deployable mesh antenna for space borne ocean salinity measurements[R].[S.l.]:International Geosciences and Remote Sensing Symposium,2000(6):2549-2551.
[10]Smith T,Lee B,Semler D,et al.A large S-band antenna for a mobile satellite[C]//Space 2004 Conference and Exhibit.San Diego,Califorhia:AIAA,2004:2317-2324.
[11]Duan Baoyan,Luo Ying.On optimization of large cablemesh surface antenna with both deployed and retracted states[R].[S.l.]:11th AIAA/ISSMO Multidisciplinary Analysis and Optimization Conference,2006:943-950.
[12]陶成,刘丽坤,周志成,等.环形桁架式天线展开不同步现象分析[J].中国空间科学技术,2015,35(1):1-8.(Tao Cheng,Liu Likun,Zhou Zhicheng,et al.Analysis of the non-synchronous phenomenon of circular truss antenna[J].Space Science and Technology in China,2015,1:1-8(in Chinese)).
[13]赵孟良.空间可展结构展开过程动力学理论分析、仿真及试验[D].杭州:浙江大学,2007:29-32.(Zhao Mengliang.Theoretical analysis,simulation and experiment of the dynamic process of deployable space deployable structure[D].Hangzhou:Zhejiang University,2007:29-32(in Chinese)).
[14]韦娟芳,赵人杰,关富玲.星载天线结构的发展趋势[J].空间电子技术,2002(1):49-54.(Wei Juanfang,Zhao Renjie,Guan Fuling.Development trend of satellite antenna structure[J].Space Electronic Technology,2002(1):49-54(in Chinese)).
[15]李团结,张琰,李涛.周边桁架可展天线展开过程动力学分析及控制[J].航空学报,2009,30(3):444-449.(Li Tuanjie,Zhang Yan,Li Tao.Dynamic analysis and control of deployable antenna deployable process[J].Aeronautical Journal,2009,30(3):444-449(in Chinese)).
[16]罗鹰,段宝岩.周边桁架式展开天线几何布局优化[J].空间科学学报,2004,24(2):132-137.(Luo Ying,Duan Baoyan.Geometric layout optimization of perimeter truss deployable antenna[J].Journal of Space Science,2004,24(2):132-137(in Chinese)).
[17]李刚,关富玲.环形桁架展开天线索网的预拉力优化技术及工程应用[J].固体力学学报,2006(增刊1):180-185.(Li Gang,Guan Fuling.Optimization of pretension in net of astromesh deployable reflector and engineering application[J].Acta Mechanica Solida Sinica,2006(S1):180-185(in Chinese)).
[18]曹树谦,张文德.振动结构模态分析:理论、实验与应用[M].天津:天津大学出版社,2001.(Cao Shuqian,Zhang Wende.Modal analysis of vibration structure:theory,experiment and application[M].Tianjin:Tianjin University Press,2001(in Chinese)).
[19]田大可.模块化空间可展开天线支撑桁架设计与实验研究[D].哈尔滨:哈尔滨工业大学,2011:29-32.(Tian Dake.Design and experimental research on truss structure for modular space deployable antenna[D].Harbin:Harbin Institute of University,2011:29-32(in Chinese)).