抛物面天线反射面形变与应力分析
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摘要
天线结构由反射面和支撑反射面的背架结构组成,其中反射面是天线发射和接收电磁信号的主要构件,其表面形状的精度直接影响着天线电磁性能的发挥。本文应用弹性力学中的薄壳理论研究抛物面天线反射面在外载作用下的变形性质,并针对工程实际中几种常见反射面的边框约束,对不同边框条件下反射面的位移场和应力场进行了计算和分析,总结了常见边框约束对反射面变形的影响特点。与以往天线结构力学分析采取数值计算方法不同的是,本文从解析法的思路出发研究天线反射面的力学性质。
分析过程中,将抛物面天线反射面看作抛物面薄壳结构,而将背架结构对反射面的支撑和约束作用简化为作用于反射面顶点处的中心体支撑和壳边处的边框约束。在对薄壳的变形方程进行了由偏微分方程转化为常微分方程、消元、积分等一系列化简后,整理为以位移法求解反射面变形的基本方程,同时提出了中心体支撑以及边框约束的边界条件,从而确立了应用解析法研究反射面变形的定解问题。
计算过程中,提出了一种幂级数方法和一种按照方程中的小参数展开进行求解的方法用以解决反射面变形方程的求解问题,分别对小口径和大口径抛物面天线反射面进行了具体算例的计算,得到了反射面位移场和应力场的解析表达式,在此基础上对反射面的变形性质进行了分析。
考虑到边框约束对反射面变形的影响,对不同边框条件下反射面的变形进行了求解和比较分析,着重总结了刚性边框和弹性边框对位移场的约束效果,及其与反射面几何参数之间的影响规律。
Antenna structure is composed of reflector and antenna frame which is used to support the reflector. Reflector is the primary component of antenna structure to send and receive electromagnetism signal. So the surface precision of reflector direct influences the electromagnetic performance of antenna. In this paper, the deformation property of reflector under loading effect is researched by elasticity theory of thin shell. The displacement and stress fields of reflectors constrained by several different types of edge in engineering are analyzed and compared, and the law of edge constraint effect on reflector's deformation property is summarized. Different from previous mechanical analysis of antenna structure, the displacement and stress fields of reflectors are obtained by analytic method in this paper.
At analyzing antenna structure's mechanical property, the reflector is seen as a thin shell model, and its constraints are simplified as a top point support and an edge constraint. After the simplification including the steps of changing partial differential equations into constant differential equations, element elimination and integral, the shell deformation equation is turned into the displacement method basic equation. And the boundary condition of top point support and edge constraint is proposed. Thus the definite problem of reflector deformation equation is established.
In calculation process, a power series method and a method based on expansion reflector deformation equation according a small parameter in the equation are used to resolve small-diameter and large-diameter paraboloid antenna reflectors deformation problem respectively. On the based of the result of displacement and stress fields, the deformation characteristic of reflector is analyzed detailedly.
For embodying the influence of edge constraint to reflector's deformation property, the deformation characteristics of reflectors constrained by free edge, rigid edge and elastic edge are all analyzed and compared in this paper, which rigid edge and elastic edge effect on reflector's displacement fields, and the relation between the effect and the geometric parameters of reflector are summarized emphatically.
分析过程中,将抛物面天线反射面看作抛物面薄壳结构,而将背架结构对反射面的支撑和约束作用简化为作用于反射面顶点处的中心体支撑和壳边处的边框约束。在对薄壳的变形方程进行了由偏微分方程转化为常微分方程、消元、积分等一系列化简后,整理为以位移法求解反射面变形的基本方程,同时提出了中心体支撑以及边框约束的边界条件,从而确立了应用解析法研究反射面变形的定解问题。
计算过程中,提出了一种幂级数方法和一种按照方程中的小参数展开进行求解的方法用以解决反射面变形方程的求解问题,分别对小口径和大口径抛物面天线反射面进行了具体算例的计算,得到了反射面位移场和应力场的解析表达式,在此基础上对反射面的变形性质进行了分析。
考虑到边框约束对反射面变形的影响,对不同边框条件下反射面的变形进行了求解和比较分析,着重总结了刚性边框和弹性边框对位移场的约束效果,及其与反射面几何参数之间的影响规律。
Antenna structure is composed of reflector and antenna frame which is used to support the reflector. Reflector is the primary component of antenna structure to send and receive electromagnetism signal. So the surface precision of reflector direct influences the electromagnetic performance of antenna. In this paper, the deformation property of reflector under loading effect is researched by elasticity theory of thin shell. The displacement and stress fields of reflectors constrained by several different types of edge in engineering are analyzed and compared, and the law of edge constraint effect on reflector's deformation property is summarized. Different from previous mechanical analysis of antenna structure, the displacement and stress fields of reflectors are obtained by analytic method in this paper.
At analyzing antenna structure's mechanical property, the reflector is seen as a thin shell model, and its constraints are simplified as a top point support and an edge constraint. After the simplification including the steps of changing partial differential equations into constant differential equations, element elimination and integral, the shell deformation equation is turned into the displacement method basic equation. And the boundary condition of top point support and edge constraint is proposed. Thus the definite problem of reflector deformation equation is established.
In calculation process, a power series method and a method based on expansion reflector deformation equation according a small parameter in the equation are used to resolve small-diameter and large-diameter paraboloid antenna reflectors deformation problem respectively. On the based of the result of displacement and stress fields, the deformation characteristic of reflector is analyzed detailedly.
For embodying the influence of edge constraint to reflector's deformation property, the deformation characteristics of reflectors constrained by free edge, rigid edge and elastic edge are all analyzed and compared in this paper, which rigid edge and elastic edge effect on reflector's displacement fields, and the relation between the effect and the geometric parameters of reflector are summarized emphatically.
引文
[1]Archer J S.High-performance parabolic antenna reflector.J Space Roc,1980,17(1):20-26
[2]Thornton E A,Paul D B.Thermal-structural analysis of large space structures:an assessment of recent advances.J Space Roc,1985,22(4):358-393
[3]Lutg L D,Allen D H,Haisler W E.Finite-element model for the thermoelastic analysis of large composite space structures.J Space Roc,1987,24(5 ):430-436
[4]李连军,戴金海.双翼箱式航天器太阳光压干扰力矩模型.航天控制,2005,23(4):13-17
[5]马洪波,陈建军等.随机参数天线结构的概率优化设计.应用力学学报,2005,22(3):491-494
[6]蒋尔进.一种圆抛物面天线的有限元分析.雷达与对抗,2004(4):61-64
[7]陈向阳,关富玲,岳键如.可展星载天线结构设计.空间结构,2000,6(4):41-46
[8]韦娟芳,赵人杰,关富玲.星载天线结构的发展趋势.空间电子技术,2002(1):400-429
[9]罗鹰,段宝岩.星载可展开天线结构现状与发展.电子机械工程,2005,21(5):49-54
[10]赵武林.天线结构力学分析中的约束方法.现代雷达,2002(3):80-83
[11]Honener S V.Honmologous deformation of tiltable telescope.J Structure Division Proc ASCE,1967,93(5):461-495
[12]Panossian H V.Model order reduction techniques in large space structure application.The 33~(rd) AIAA/ASME/ASCE/AHS/ASC Structural Dynamics and Material Conference,1992,13-15
[13]Levy R.Computer-aided design of antenna structures and componets.Computers &Structures,1976,6(4/5):419-428
[14]王生洪,李志良,汪勤悫.大型天线结构的保型优化设计.固体力学学报,1981,2(1):12-26
[15]史可信、万邦志.雷达天线结构刚度优化设计.兵工学报,1982,(3):26-32
[16]段宝岩,叶尚辉,天线结构的几何优化设计的一种结合法.计算结构力学及其应用,1986,3(3):57-65
[17]陈树勋,王光远.天线结构多目标模糊优化设计.计算结构力学及其应用, 1991,8(4):413-420
[18]DuanB Y,Qi Y H,Xu G H,ed.Study on optimizaion of mechanicaland electrcnic synthesis for the antenna structural system.Int J Mechatronics,1994,4(6):553-564
[19]陈建军,戴宝华.天线反射面精度和结构体系的可靠性分析.应用力学学报,1990,7(1):56-65
[20]Chen J J,Dai B H.Optimum design of antenna structure based on reliability.Acta Electronica Sinica,1989,(Supplement):44-54
[21]陈建军,高伟等.多工况下天线结构的可靠性优化设计.机械科学与技术,2002,21(3):373-375
[22]Fanson J L,Garba J A.Experimental studies of active members in control of large space structures.Proceedings of the 29~(th) AIAA/SDM conference,1988,AIAA-88-2207:9-17
[23]Chen G S,Lurie B J.Wada B K.Experimental studies of adaptive st ructures for precision performance.Proceedings of the 30~(th) AIAA/SDM conference,1989,AIAA-89-1327- CP:1462-1472
[24]Fanson J L,Blackwood G H,Chu C C.Active member control of precision structures.Proceedings of the 30~(th) AIAA/ SDM conference,1989,AIAA-89-1329- CP:1480-1494
[25]王永,马运领等.智能抛物面桁架天线的建模和模阶降低.中国科学技术大学学报,2005,35(4):530-536
[26]Garba J A,Wada B K.Fanson J L.Aaaptive structures for precision controlled larse space system.Journal of Intelligent Material Systems and Structures,1992,3(2):348-366
[27]Au T M,Luk R M.Fanson J L.Eeffect of Parasitic element on the characteristics of microstrip antennas.IEEE Transaction on Antennas Propaqat,1991,39:1244-1251
[28]Koconis B,Kollar L P.Shape control of composite plates and shells with embedded actuators Ⅱ Desired Shape Specified.Journal of Composite Materials,1994,(28):262-285
[29]Furuya H,Haftka R T.Static shape control of space trusses with partial measurements,.Journal of Spacecraft and Rockets,1995,32(5):856-865
[30]Kiely E,Washington G,Bernhard J.Design and Development of Smart Microstrip Patch Antennas.Smart Materials and Structures,1998,(7):792-800
[31]Washington G.Smart aperture antennas.Smart Materials and Structures,1996,5:801-805
[32]Yoon H S,Washington G,Theunissen W H.Analysis and design of doubly curvecl piezoelectric strip-actuated aperture antennas.IEEE Transation on Antennas and Propaqation,2000,48(5):755-762
[33]Rogers C A.Intelligent Materials Systems:the Dawn of a New Materials Age.J Intell Mater Sys & Struct,1993,(4):4-12
[34]Saravanan U,Sivakumar S M,Ralyanaraman V.A study on the design and behavior of smart antenna.Smart Materials and Structures,2001,(10):580-598
[35]聂润兔,邵成勋,邹振祝,自适应桁架形状控制中主动杆多目标最优控制.应用力学学报,1997,14(3):48-53
[36]姚国风,陈塑寰.抛物面天线的智能静态形状控制.吉林大学自然科学学报,2000,30(4):75-78
[37]隋允康,邵建义.自适应超静定桁架结构强度控制的研究.固体力学学报,2001,22(2):136-142
[38]隋允康,龙连春.智能天线结构形状最优控制.无线电通讯技术,2003,29(5):25-27
[39]龙连春,隋允康.自适应天线结构位置最优控制.工程力学,2005,22(2):236-240
[40]隋允康,龙连春.智能抛物面天线多目标最优控制.计算力学学报,2005,22(6):671-676
[41]阳志春,龙连春,隋允康.智能抛物面天线分层序列最优控制.强度与环境,2006,33(4):49-54
[42]毕明路.7m天线的数字化建模及静、动态分析.天线应用,2003,29(3):34-35
[43]毕明路.风的模拟及抛物面天线的风荷响应.计算机仿真,2003,20(8):400-429
[44]周生怀,周芸.力学分析、预调技术及其在工程中的应用.现代电子技术,2003,151(8):66-68
[45]刘宇,贾建援.某型号天线座壳体强度刚度有限元分析.雷达与对抗,2005(3):45-47
[46]周瑞兴,上官云信,高永卫.圆锥和抛物面天线的风荷载及变形特性分析.现代雷达,2002,24(2):76-79
[47]Chen J J,Che J W,Sun H A,ed.Probabilistic dynamic analysis of truss structures.Structural Engineering and Mechanics,2002,13(2):231-239
[48]Zhao L,Chen Q.Neumann dynamic stochastic finite element method of vibration for structures with stochastic parameters to random excitation.Computers and Structures,2000,77(6):651-657
[49]Gao W,Chen J J,Ma H B,ed.Optimal placement of active bars in active vibration control for piezoelectric intelligent truss structures with random parameters.Computers and Structures,2003,81(1):53-60
[50]Rao S S,Sawyer J P.Fuzzy finite element approach for the analysis of imprecisely defined systems.AIAA Journal,1995,33(12):2364-2370
[51]梁震涛,陈建军,张建国.天线结构动力特性分析的未确知因子法.兵工学报,2007,28(4):440-444
[52]Sinton S,Rahmat S Y.Random surface error effects on offset cylindrical reflector antennas.IEEE Transactions on Antennas and Propagation,2003,51(6):1331-1337
[53]Belvin W K,Edighoffer H H,Herstrom C L.Quasi-static shape adjustment of a 15 meter diameter space antenna.Proceedings of the AIAA/ASME/ASCE/AHS 28~(th) Structures Structural Dynamics and Materials Conference,1987:705-713
[54]Boa G A,Letrou C.Fast radiation pattern evaluation for lens and reflector antennas.IEEE Transactions on Antennas and Propagation,2003,51(5):1063-1068
[55]王从思,段宝岩等.一种抛物面天线形状误差的合理评价方法.上海理工大学学报,2006,28(1):14-18
[56]徐芝纶.弹性力学(下册).第三版.北京:高等教育出版社,1990.
[57]叶尚辉,李在贵.天线结构设计.陕西:西北电讯工程学院出版社,1986.
[58]De Jager E M,Jiang Furu.The Theory of Singular Perturbation.Amsterdam:North -Holland Publishing Co,1996.
[59]Han X L.Singular Perturbations of Boundary Value Problem for a Class of Quasilinear Differential Equations.J of Math,2003,18(2):192-197
[60]Tang R R.The Boundary Layer Problems for a Class of Fourth Order Nonlinear Singularly Perturbed Equations.J of Math,2007,27(4):385-390
[61]张宇力,曾广武.鞍形旋转壳在轴对称载荷作用下的一种新算法.武汉大学学报,2003,36(5):115-117
[2]Thornton E A,Paul D B.Thermal-structural analysis of large space structures:an assessment of recent advances.J Space Roc,1985,22(4):358-393
[3]Lutg L D,Allen D H,Haisler W E.Finite-element model for the thermoelastic analysis of large composite space structures.J Space Roc,1987,24(5 ):430-436
[4]李连军,戴金海.双翼箱式航天器太阳光压干扰力矩模型.航天控制,2005,23(4):13-17
[5]马洪波,陈建军等.随机参数天线结构的概率优化设计.应用力学学报,2005,22(3):491-494
[6]蒋尔进.一种圆抛物面天线的有限元分析.雷达与对抗,2004(4):61-64
[7]陈向阳,关富玲,岳键如.可展星载天线结构设计.空间结构,2000,6(4):41-46
[8]韦娟芳,赵人杰,关富玲.星载天线结构的发展趋势.空间电子技术,2002(1):400-429
[9]罗鹰,段宝岩.星载可展开天线结构现状与发展.电子机械工程,2005,21(5):49-54
[10]赵武林.天线结构力学分析中的约束方法.现代雷达,2002(3):80-83
[11]Honener S V.Honmologous deformation of tiltable telescope.J Structure Division Proc ASCE,1967,93(5):461-495
[12]Panossian H V.Model order reduction techniques in large space structure application.The 33~(rd) AIAA/ASME/ASCE/AHS/ASC Structural Dynamics and Material Conference,1992,13-15
[13]Levy R.Computer-aided design of antenna structures and componets.Computers &Structures,1976,6(4/5):419-428
[14]王生洪,李志良,汪勤悫.大型天线结构的保型优化设计.固体力学学报,1981,2(1):12-26
[15]史可信、万邦志.雷达天线结构刚度优化设计.兵工学报,1982,(3):26-32
[16]段宝岩,叶尚辉,天线结构的几何优化设计的一种结合法.计算结构力学及其应用,1986,3(3):57-65
[17]陈树勋,王光远.天线结构多目标模糊优化设计.计算结构力学及其应用, 1991,8(4):413-420
[18]DuanB Y,Qi Y H,Xu G H,ed.Study on optimizaion of mechanicaland electrcnic synthesis for the antenna structural system.Int J Mechatronics,1994,4(6):553-564
[19]陈建军,戴宝华.天线反射面精度和结构体系的可靠性分析.应用力学学报,1990,7(1):56-65
[20]Chen J J,Dai B H.Optimum design of antenna structure based on reliability.Acta Electronica Sinica,1989,(Supplement):44-54
[21]陈建军,高伟等.多工况下天线结构的可靠性优化设计.机械科学与技术,2002,21(3):373-375
[22]Fanson J L,Garba J A.Experimental studies of active members in control of large space structures.Proceedings of the 29~(th) AIAA/SDM conference,1988,AIAA-88-2207:9-17
[23]Chen G S,Lurie B J.Wada B K.Experimental studies of adaptive st ructures for precision performance.Proceedings of the 30~(th) AIAA/SDM conference,1989,AIAA-89-1327- CP:1462-1472
[24]Fanson J L,Blackwood G H,Chu C C.Active member control of precision structures.Proceedings of the 30~(th) AIAA/ SDM conference,1989,AIAA-89-1329- CP:1480-1494
[25]王永,马运领等.智能抛物面桁架天线的建模和模阶降低.中国科学技术大学学报,2005,35(4):530-536
[26]Garba J A,Wada B K.Fanson J L.Aaaptive structures for precision controlled larse space system.Journal of Intelligent Material Systems and Structures,1992,3(2):348-366
[27]Au T M,Luk R M.Fanson J L.Eeffect of Parasitic element on the characteristics of microstrip antennas.IEEE Transaction on Antennas Propaqat,1991,39:1244-1251
[28]Koconis B,Kollar L P.Shape control of composite plates and shells with embedded actuators Ⅱ Desired Shape Specified.Journal of Composite Materials,1994,(28):262-285
[29]Furuya H,Haftka R T.Static shape control of space trusses with partial measurements,.Journal of Spacecraft and Rockets,1995,32(5):856-865
[30]Kiely E,Washington G,Bernhard J.Design and Development of Smart Microstrip Patch Antennas.Smart Materials and Structures,1998,(7):792-800
[31]Washington G.Smart aperture antennas.Smart Materials and Structures,1996,5:801-805
[32]Yoon H S,Washington G,Theunissen W H.Analysis and design of doubly curvecl piezoelectric strip-actuated aperture antennas.IEEE Transation on Antennas and Propaqation,2000,48(5):755-762
[33]Rogers C A.Intelligent Materials Systems:the Dawn of a New Materials Age.J Intell Mater Sys & Struct,1993,(4):4-12
[34]Saravanan U,Sivakumar S M,Ralyanaraman V.A study on the design and behavior of smart antenna.Smart Materials and Structures,2001,(10):580-598
[35]聂润兔,邵成勋,邹振祝,自适应桁架形状控制中主动杆多目标最优控制.应用力学学报,1997,14(3):48-53
[36]姚国风,陈塑寰.抛物面天线的智能静态形状控制.吉林大学自然科学学报,2000,30(4):75-78
[37]隋允康,邵建义.自适应超静定桁架结构强度控制的研究.固体力学学报,2001,22(2):136-142
[38]隋允康,龙连春.智能天线结构形状最优控制.无线电通讯技术,2003,29(5):25-27
[39]龙连春,隋允康.自适应天线结构位置最优控制.工程力学,2005,22(2):236-240
[40]隋允康,龙连春.智能抛物面天线多目标最优控制.计算力学学报,2005,22(6):671-676
[41]阳志春,龙连春,隋允康.智能抛物面天线分层序列最优控制.强度与环境,2006,33(4):49-54
[42]毕明路.7m天线的数字化建模及静、动态分析.天线应用,2003,29(3):34-35
[43]毕明路.风的模拟及抛物面天线的风荷响应.计算机仿真,2003,20(8):400-429
[44]周生怀,周芸.力学分析、预调技术及其在工程中的应用.现代电子技术,2003,151(8):66-68
[45]刘宇,贾建援.某型号天线座壳体强度刚度有限元分析.雷达与对抗,2005(3):45-47
[46]周瑞兴,上官云信,高永卫.圆锥和抛物面天线的风荷载及变形特性分析.现代雷达,2002,24(2):76-79
[47]Chen J J,Che J W,Sun H A,ed.Probabilistic dynamic analysis of truss structures.Structural Engineering and Mechanics,2002,13(2):231-239
[48]Zhao L,Chen Q.Neumann dynamic stochastic finite element method of vibration for structures with stochastic parameters to random excitation.Computers and Structures,2000,77(6):651-657
[49]Gao W,Chen J J,Ma H B,ed.Optimal placement of active bars in active vibration control for piezoelectric intelligent truss structures with random parameters.Computers and Structures,2003,81(1):53-60
[50]Rao S S,Sawyer J P.Fuzzy finite element approach for the analysis of imprecisely defined systems.AIAA Journal,1995,33(12):2364-2370
[51]梁震涛,陈建军,张建国.天线结构动力特性分析的未确知因子法.兵工学报,2007,28(4):440-444
[52]Sinton S,Rahmat S Y.Random surface error effects on offset cylindrical reflector antennas.IEEE Transactions on Antennas and Propagation,2003,51(6):1331-1337
[53]Belvin W K,Edighoffer H H,Herstrom C L.Quasi-static shape adjustment of a 15 meter diameter space antenna.Proceedings of the AIAA/ASME/ASCE/AHS 28~(th) Structures Structural Dynamics and Materials Conference,1987:705-713
[54]Boa G A,Letrou C.Fast radiation pattern evaluation for lens and reflector antennas.IEEE Transactions on Antennas and Propagation,2003,51(5):1063-1068
[55]王从思,段宝岩等.一种抛物面天线形状误差的合理评价方法.上海理工大学学报,2006,28(1):14-18
[56]徐芝纶.弹性力学(下册).第三版.北京:高等教育出版社,1990.
[57]叶尚辉,李在贵.天线结构设计.陕西:西北电讯工程学院出版社,1986.
[58]De Jager E M,Jiang Furu.The Theory of Singular Perturbation.Amsterdam:North -Holland Publishing Co,1996.
[59]Han X L.Singular Perturbations of Boundary Value Problem for a Class of Quasilinear Differential Equations.J of Math,2003,18(2):192-197
[60]Tang R R.The Boundary Layer Problems for a Class of Fourth Order Nonlinear Singularly Perturbed Equations.J of Math,2007,27(4):385-390
[61]张宇力,曾广武.鞍形旋转壳在轴对称载荷作用下的一种新算法.武汉大学学报,2003,36(5):115-117