水下超空泡航行体结构稳定与动力可靠性研究
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摘要
由于超空泡航行体结构一般为细长体，并且航行体在高速运动时所受的轴向力和尾部冲击力非常大，因此航行体结构在这些载荷的作用下极易受到破坏。长期以来人们对超空泡航行体结构的振动特性进行了大量的理论分析和试验研究,取得了一些重要的研究成果。然而,这些研究大多都忽略了结构的物理和几何参数的随机性的影响。但在实际的操作过程中,由于材料特性的随机性，以及航行体结构在制造、安装过程中可能会受到各种各样随机因素的影响,这些因素都会对结构动力特性产生一定的影响。因此，研究具有随机参数的超空泡航行体结构的动力稳定性，以及航行体结构的动力可靠性是很有意义的，本文的主要内容如下：
1、建立了超空泡航行体稳定滑行和局部空泡运动状态时的平衡方程，得到了空化器和尾部受力的平衡关系式，通过迭代得到了航行体角度的平衡值。最后比较了超空泡的两种基本形态模型，分析了不同参数条件下两种空泡模型的变化规律。针对超空泡航行体入水时的水动力特征，给出了超空泡航行体入水时不稳定空泡形状的表达式。
2、针对超空泡射弹水下高速航行时前端空化器受纵向随机载荷作用时的动力稳定性问题，建立超空泡射弹结构的运动偏微分方程。根据Bolotin方法，给出了超空泡射弹的动力不稳定性区域。
3、当考虑超空泡射弹结构在加工、安装过程中存在的误差等不确定性因素，利用随机因子法求出随机参数超空泡射弹结构的动力不稳定区域边界。应用代数综合法，得到了含随机参数的超空泡射弹动力不稳定区域边界的数字特征（均值和方差）。并分析了参数的随机性对射弹结构动力不稳定性的影响。数值计算表明，参数的随机性对超空泡射弹动力不稳定性有一定的影响，本文的方法可为随机参数超空泡射弹的设计提供参考。
4、对于具有随机参数的超空泡鱼雷结构在随机激励下的动力可靠性问题，使用八节点超参数壳单元对超空泡鱼雷建模。将超空泡鱼雷尾部受到的冲击载荷及滑行力，简化成两个存在某一相位差的平稳随机过程，并考虑冲击力与滑行阻力之间的相关性,利用虚拟激励法将超空泡鱼雷所受的随机过程载荷精确地转化成确定性简谐载荷问题。
5、应用Newmark法结合虚拟激励摄动法计算出随机结构的随机应力响应，进而求出随机参数超空泡鱼雷结构动力可靠性所需的全部数字特征。由首次超越破坏准则，得到了随机参数超空泡鱼雷结构动力可靠度的均值和方差，解决了具有随机参数的超空泡鱼雷结构的动力可靠性问题。
Because the structure of supercavity vehicle generally has to be designed as slenderconfiguration, and the high longitudinal force and the tail impact force are both very likely tolead to the structure of supercavity vehicle in damage. A large number of theory analysis andexperimental research have been made on structural vibration characteristics of supercavityvehicle, and people had made some important research results. However, these studies did nottake into account the randomness of physical and geometrical parameters of structure. But inactual operation process, because the randomness of the material properties, as well as thestructure of supercavity vehicle may subject to the effect of various random factors in themanufacture, installation processes, they are all produce certain effect on dynamiccharacteristics of structure.So it is necessary to research dynamic stability and reliability onthe structure of supercavity vehicle with stochastic parameters. The major content of thethesis as follows:
1. The equilibrium equation when supercavity vehicle in the steady-state motion and inthe partial cavitaion regime were established, and the relations for the balanced forces on thecavitator and the tail were obtained, The balanced values of the angles are founded by theiteration process, At last we analysis the changing regularity of the two cavity models bycomparing the two basic form models under the conditions of the different parameters.According to the hydrodynamic characteristic when the supercavity vehicle enters into water,we can infer the calculating formula of the unsteady cavity configuration.
2. Taking aim at the problems of dynamic stability when the head of supercavitatingprojectile subject to the axial random load at high speed motion underwater, the dynamicpartial differential equation of supercavitating projectile structure was established, then thenumerical calculation for the dynamic stability of supercavitating structure was performedwith Bolotin method.
3. In consideration of the stochastic parameters, the regions of dynamic instability ofprojectile with stochastic parameters were constructed based on the random factor method,the mean value and the variance of the boundary of dynamic instable regions were thenderived by using the random variable’s algebra synthesis method. The influence of stochasticparameters on the dynamic instability of supercavitating projectile was also analyzed. The computational results indicated that the stochastic parameters have certain influence on thedynamic instability. The results provided a certain theoretical foundation for the design ofsupercavitating projectile.
4. Dynamic reliability of stochastic parameters supercavitating torpedo under the randomexcitation is investigated. The supercavitating torpedo is modeled by using eight-nodesuper-parametric shell elements. The impact loads and planing forces of the tail onsupercavitating torpedo structures are simplified into two stationary random processes with acertain phase difference, and considering the correlation between the impact loads and planingforces of the tail on supercavitating torpedo structures, the random excitations are transformedinto sinusoidal ones in terms of the pseudo excitation method.
5. The structural stress response can be obtained through combining Newmark methodwith pseudo excitation perturbation method, and then all required digital features for dynamicreliability of supercavitating torpedo have be calculated. The expressions of the mean valueand the variance of stochastic supercavitating torpedo dynamic reliability are educed from thefist excursion probability mechanism of calculating dynamic reliability, the structure dynamicreliability problems of supercavitating torpedo with random parameter have be solved. Finally,the method of this paper was proved feasible and available comparing with the Monte Carlomethod by an example.
1、建立了超空泡航行体稳定滑行和局部空泡运动状态时的平衡方程，得到了空化器和尾部受力的平衡关系式，通过迭代得到了航行体角度的平衡值。最后比较了超空泡的两种基本形态模型，分析了不同参数条件下两种空泡模型的变化规律。针对超空泡航行体入水时的水动力特征，给出了超空泡航行体入水时不稳定空泡形状的表达式。
2、针对超空泡射弹水下高速航行时前端空化器受纵向随机载荷作用时的动力稳定性问题，建立超空泡射弹结构的运动偏微分方程。根据Bolotin方法，给出了超空泡射弹的动力不稳定性区域。
3、当考虑超空泡射弹结构在加工、安装过程中存在的误差等不确定性因素，利用随机因子法求出随机参数超空泡射弹结构的动力不稳定区域边界。应用代数综合法，得到了含随机参数的超空泡射弹动力不稳定区域边界的数字特征（均值和方差）。并分析了参数的随机性对射弹结构动力不稳定性的影响。数值计算表明，参数的随机性对超空泡射弹动力不稳定性有一定的影响，本文的方法可为随机参数超空泡射弹的设计提供参考。
4、对于具有随机参数的超空泡鱼雷结构在随机激励下的动力可靠性问题，使用八节点超参数壳单元对超空泡鱼雷建模。将超空泡鱼雷尾部受到的冲击载荷及滑行力，简化成两个存在某一相位差的平稳随机过程，并考虑冲击力与滑行阻力之间的相关性,利用虚拟激励法将超空泡鱼雷所受的随机过程载荷精确地转化成确定性简谐载荷问题。
5、应用Newmark法结合虚拟激励摄动法计算出随机结构的随机应力响应，进而求出随机参数超空泡鱼雷结构动力可靠性所需的全部数字特征。由首次超越破坏准则，得到了随机参数超空泡鱼雷结构动力可靠度的均值和方差，解决了具有随机参数的超空泡鱼雷结构的动力可靠性问题。
Because the structure of supercavity vehicle generally has to be designed as slenderconfiguration, and the high longitudinal force and the tail impact force are both very likely tolead to the structure of supercavity vehicle in damage. A large number of theory analysis andexperimental research have been made on structural vibration characteristics of supercavityvehicle, and people had made some important research results. However, these studies did nottake into account the randomness of physical and geometrical parameters of structure. But inactual operation process, because the randomness of the material properties, as well as thestructure of supercavity vehicle may subject to the effect of various random factors in themanufacture, installation processes, they are all produce certain effect on dynamiccharacteristics of structure.So it is necessary to research dynamic stability and reliability onthe structure of supercavity vehicle with stochastic parameters. The major content of thethesis as follows:
1. The equilibrium equation when supercavity vehicle in the steady-state motion and inthe partial cavitaion regime were established, and the relations for the balanced forces on thecavitator and the tail were obtained, The balanced values of the angles are founded by theiteration process, At last we analysis the changing regularity of the two cavity models bycomparing the two basic form models under the conditions of the different parameters.According to the hydrodynamic characteristic when the supercavity vehicle enters into water,we can infer the calculating formula of the unsteady cavity configuration.
2. Taking aim at the problems of dynamic stability when the head of supercavitatingprojectile subject to the axial random load at high speed motion underwater, the dynamicpartial differential equation of supercavitating projectile structure was established, then thenumerical calculation for the dynamic stability of supercavitating structure was performedwith Bolotin method.
3. In consideration of the stochastic parameters, the regions of dynamic instability ofprojectile with stochastic parameters were constructed based on the random factor method,the mean value and the variance of the boundary of dynamic instable regions were thenderived by using the random variable’s algebra synthesis method. The influence of stochasticparameters on the dynamic instability of supercavitating projectile was also analyzed. The computational results indicated that the stochastic parameters have certain influence on thedynamic instability. The results provided a certain theoretical foundation for the design ofsupercavitating projectile.
4. Dynamic reliability of stochastic parameters supercavitating torpedo under the randomexcitation is investigated. The supercavitating torpedo is modeled by using eight-nodesuper-parametric shell elements. The impact loads and planing forces of the tail onsupercavitating torpedo structures are simplified into two stationary random processes with acertain phase difference, and considering the correlation between the impact loads and planingforces of the tail on supercavitating torpedo structures, the random excitations are transformedinto sinusoidal ones in terms of the pseudo excitation method.
5. The structural stress response can be obtained through combining Newmark methodwith pseudo excitation perturbation method, and then all required digital features for dynamicreliability of supercavitating torpedo have be calculated. The expressions of the mean valueand the variance of stochastic supercavitating torpedo dynamic reliability are educed from thefist excursion probability mechanism of calculating dynamic reliability, the structure dynamicreliability problems of supercavitating torpedo with random parameter have be solved. Finally,the method of this paper was proved feasible and available comparing with the Monte Carlomethod by an example.
引文
[1]杨莉,张庆明.超空泡技术的应用现状和发展趋势.战术导弹技术.2006,(5):6-10页
[2] Savchenko Yu N, Semenenko V N, ed. Unsteady super-cavitated motion of bodies.International Journal of Fluid Mechanics Research,2000,27(1):109-137P
[3] Vasin A D. Application of the Slender Body Theory to Investigation of the DevelopedAxially Symmetric Cavitation Flows in a Subsonic Steam of Compressible Fluid.International Journal of Fluid Mechanics Research,2001,28(5):702-716P
[4] Semenenko V N. Calculation of Two-Dimensional Unsteady Supercavities atArbitrary Time Dependence. International Journal of Fluid Mechanics Research,2004,31(6):621-632P
[5]袁绪龙,张宇文,王育才等.水下航行体通气超空泡非对称性研究.力学学报.2004,36(2):146-150页
[6]贾力平,于开平,张嘉钟,王聪等.空化器参数对空泡形成和发展的影响.力学学报.2007,39(2):210-216页
[7] Foote J P, Lineberry J T. Investigation of aluminum particle combustion forunderwater propulsion applications.ASME/SAE/ASEE,32nd Joint PropulsionConference and Exhibit, Lake Buena Vista, FL, July1-3,1996．
[8]田维平,蔡体敏,陆贺建,高波.水冲压发动机热力计算．固体火箭技术.2006,29(2):95-98页
[9]郜冶，贺征，刘平安．超空泡推进发动机燃料能量特性比较．固体火箭技术．2009，32(1)：27-32页
[10] Ruzzene M, Kamada R,ed. Trajectory Optimization Strategies for SupercavitatingUnderwater Vehicles. Journal of Vibration and Control,2008,14(5):611-644P
[11]冯光,颜开.超空泡航行体水下弹道的数值计算.船舶力学.2005,9(2):1-8页
[12]蒋运华,安伟光,安海.初始扰动下水下超高速运动体弹道数值模拟.水动力学研究与进展.2008,23(5):571-579页
[13] Dzielski J, Kurdila A. A Benchmark Control Problem for Supercavitating Vehicles andan Initial Investigation of Solutions. Journal of Vibration and Control,2003,9(7):791-804P
[14]魏英杰,王京华,张嘉钟等.水下超空泡航行体非线性动力学与控制.振动与冲击.2009,28(6):179-204页
[15]赵新华,孙尧,莫宏伟,李雪莲.水下超高速航行体纵向运动的控制方法研究.工程力学.2009,26(2):242-256页
[16] Vasin A D. Some Problems of Supersonic Cavitation Flows. In: Proceeding of the4thInternational Symposium on Cavitation, Pasadena CA,20-23June2001:1-13P
[17] Ruzzene M. Dynamic buckling of periodically stiffened shells: application tosupercavitating vehicles. International Journal of Solids and Structures,2004(41):1039-1059P
[18] Ruzzene M. Non-axisymmetric buckling of stiffened supercavitating shells: static anddynamic analysis. Computers&Structures,2004(82):257-269P
[19] Ruzzene M, Soranna F. Impact Dynamics of Elastic Stiffened Supercavitatingunderwater Vehicles. Journal of Vibration and Control,2004(10):243-267P
[20] Ahn S S, Ruzzene M. Optimal design of cylindrical shells for enhanced bucklingstability: Application to supercavitating underwater vehicles. Finite Elements inanalysis and design,2006(42):967-976P
[21] Choi J Y, Ruzzene M. Stability analysis of supercavitating underwater vehicles withadaptive cavitator. International Journal of Mechanical Sciences,2006(48):1360-1370P
[22] Alyanak Edward, Venkayya Vipperla, ed. Structural response and optimization of asupercavitating torpedo. Finite Elements Analysis,2005(6):563-582P
[23] Alyanak Edward, Venkayya Vipperla, ed. Structural response of a supercavitatingtorpedo shell.45th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics&Materials Conference,19-22April2004:1-8P
[24] Alyanak Edward, Venkayya Vipperla, ed. Variable shape cavitator design for asupercavitating torpedo.10th AIAA/ISSMO Multidisciplinary Analysis andOptimization Conference,30August-1September2004:1-26P
[25] Alyanak Edward, Grandhi Ramana, ed. Optimum design of a supercavitating torpedoconsidering overall size, shape, and structural configuration. International Journal ofSolids and Structures,2006(43):642-657P
[26] Choi J H, Penmetsa R C, ed. Shape optimization of the cavitator for a supercavitatingtorpedo. Struct Multidisc Optim,2005(29):159~167P.
[27] Edward Alyanak, ed. Cavitator Design for a Supercavitating Torpedo using EvidenceTheory for Reliability Estimation. Multidisciplinary Design Optimization for HighReliability and Robustness,2006:42-50P
[28]杨传武,王安稳.超空泡水下航行体振动特性分析.海军工程大学学报.2008,20(4):12-14页
[29]杨传武,王安稳.动态轴向载荷对超空泡航行体振动特性的影响.华中科技大学学报.2008,36(12):71-74页
[30]杨传武,刘刚,王安稳.超空泡体结构响应问题的有限元分析.海军工程大学学报.2008,20(2):101-104页
[31]杨传武,王安稳.冲击载荷作用下超空泡水下航行体的结构响应.华中科技大学学报.2008,36(7):129-132页
[32] Guang-ping Tian, Wei-guang An, Ling Zhou. Structure reliability analysis based onsupercavity vehicle steady motion. Journal of Harbin Institute of Technology (NewSeries),2009,16(2):251-254P
[33]麻震宇，胡凡，陈广南，张为华.超空泡航行体双层壳结构动力稳定性分析.国防科技大学学报.2011,33（4）：43-47页
[34]张劲生，张嘉钟，王聪，魏英杰.超空泡射弹结构响应的流固耦合仿真研究.船舶力学.2011,15（7）：763-768页
[35]张劲生，张嘉钟，魏英杰，王聪.超空泡射弹尾部冲击载荷的仿真研究.哈尔滨工业大学学报.2011,43（7）:19-22页
[36]张劲生,张嘉钟，魏英杰，曹伟.超空泡水下航行体的结构动力响应特性.北京航空航天大学学报.2010,36(4):411-414页
[37]孟庆昌,张志宏,顾建农,刘巨斌.超空泡射弹尾拍分析与计算.爆炸与冲击.2009,29（1）：56-60页
[38]顾永维,安伟光,安海.水下高速运动体的抗弯稳定可靠性分析.哈尔滨工程大学学报.2008,29(7):683-686页
[39]安伟光,顾永维,安海.初偏心影响下的水下高速运动体的抗弯稳定性及可靠性分析.兵工学报.2008,29(7):824-828页
[40]周凌,安伟光,安海.超空泡运动体强度与稳定性的非概率可靠性分析.哈尔滨工程大学学报.2009,30(4):362-367页
[41]周凌，安伟光，蒋运华，贾宏光.超空泡运动体圆柱薄壳屈曲可靠性分析.船舶力学.2011,15（7）：769-775页
[42] Wei-guang AN, Ling ZHOU, Hai AN. Structure buckling and non-probabilisticreliability analysis of supercavitating vehicles. Journal of Harbin Institute ofTechnology (New Series),2009,16(4):561-569P
[43]施连会,王安稳.轴向载荷下超空泡航行体动力稳定性的数值研究.振动与冲击.2011,30(2):55-59页
[44] Coodier J N, Dynamic Plastic Buckling in Dynamic Stability of Structure. ByHermann, G.1967:189-211P
[45] Gilat R, Feldman E.and Abordi J. Axisymmetric response of nonlinearly elasticcylindrical shells to dynamic axial laods, int.J. Impact Eng.,1993,13(4):545-554P
[46] Thomas J, Abbas B A H. Dynamic Stability of Timoshenk beams by Finite ElementMethod. Journal of Engineering for Industry,1976:1145-1149P
[47] Gurkan Sakar, Mustafa Sabuncu. Buckling and dynamic stability of a rotatingpretwisted asymmetric cross-section blade subjected to an axial periodic force. FiniteElements in Analysis and Design,2004:1399-1415P
[48] Briseghella L, Majorana C E, Pellegrino C. Dynamic stability of elastic structures: afinite element approach. Computers and Structures,1998:11-25P
[49] Movchan A A. The direct method of Liapunov in stability problems of elastic systems.J Appl Mach.1959,23:670-686P
[50] Movchan A A. Stability of processes with respect to two metrics. J Appl Mach Mech.1959,24:1506-1524P
[51] Leipholz H. Stability of Elastic Systems. Amsterdam: Leyden Noordhoff,1980:1-20P
[52] Budiansky B, Roth R S. Axisymmetric dynamic buckling of clamped shallow.NASA-TN-1510,1962:597-609P
[53] Hsu C S. On dynamic stability of elastic bodies with prescribed initial condition. Int JEng Sci,1966,4:1-21P
[54] Hsu C S. Stability of shallow Arches Against Snap-Through under Timewise Steploads. JAM,1968,35:31-39P
[55] Johnson E R, Mcivor I K. The effect of spatial distribution on dynamic snap-through.JAM,1987,45:612-618P
[56] Akkas N. Asymmetric buckling behavior of spherical caps under uniform step Pressure.JAM,1972,39:293-294P
[57] Butter T A, Baker W E, Babcock C D. Structural dynamics. Impact and Vibrat ion,Bulltion:1986:157-165P
[58] Goodier J N. Dynamic plastic buckling. In: Herrmann G ed. Dynamic stability ofstructure,1967:189-211P
[59]孙强，张本福.直杆的动力稳定性分析（Ⅰ）.安徽建筑工业学院学报.1996,4（1）：38-43页
[60]孙强，张本福.直杆的动力稳定性分析（Ⅱ）.安徽建筑工业学院学报.1996,4（2）：14-18页
[61]孙强，张本福.直杆的动力稳定性分析（Ⅲ）.安徽建筑工业学院学报.1996,4（3）：46-49页
[62]孙强.不同截面形状和材料柱的动力稳定性研究.工业建筑.2004,34(3):46-53页
[63]戴保东,郭秀峰,梁贵义.初弯曲对杆件动力性能的影响.山西机械.2000,3:37-38页
[64]曲淑英.大型空间框架结构的动力稳定性分析.世界地震工程.1998,14(3):44-48页
[65]李杰,郑凯锋.考虑大挠度效应及初偏心的压杆稳定性分析.昆明理工大学学报.2005,30(4):59-62页
[66]于龙文,杨乃山,陆阳南.考虑剪切影响时结构的动力稳定分析.抚顺石油学院学报.1996,16(1):27-32页
[67]童乐为，周国梁.偏心周期荷载作用下闭口薄壁构件的动力稳定性.上海力学.1992,12（2）：41-48页
[68]杨平,孙兰.偏心周期载荷作用下薄壁构件的动力稳定性.武汉交通科技大学学报.1998,22(4):403-407页
[69]杜文风,高博青,董石麟,谢忠良.一种判定杆系结构动力稳定的新方法——应力变化率法.浙江大学学报.2006,40(3):506-509页
[70]陆阳南.在纵向共振下结构的横向动力稳定分析.大连水产学院学报.1997,12(2):49-57页
[71]冯志华,胡海岩.轴向基础窄带随机激励柔性梁的稳定性与Hopf分岔.振动工程学报.2006,19(2):150-155页
[72]冯志华,芮延年,朱晓东,兰向军,张炜.轴向基础窄带随机激励悬臂梁的稳定性.动力学与控制学报.2004,2(2):74-78页
[73]高伟，陈建军，刘伟.随机参数智能桁架结构动力特性分析.应用力学学报.2003,20(l):123-127页
[74]戴君，陈建军，马洪波，崔明涛.随机参数结构在随机和在激励下的动力响应分析.工程力学.2002,19(3):64-68页
[75]高伟,陈建军.线性随机结构的平稳随机响应分析,应用力学学报.2003，20(3):92-95页
[76]欧进萍，王光远．结构随机振动.第一版．高等教育出版社，1998：347-359页
[77]朱位秋．随机振动．第一版．科学出版社，1992：249-369页
[78]李创第．李桂青，黄任常．连续随机结构的动力反应和可靠性分析．广西工学院学报.1997,8(l):25-31页
[79]石少卿．姜节胜.非平稳随机激励作用下多自由度体系系统动力可靠性研究应用力学学报.1999,16(4)：73-77页
[80]郑忠双．结构随机响应分析及其动力可靠性研究现状及趋势．福建建筑.2002,76(l):25-28页
[81]肖梅玲，高春涛，叶燎原．结构地震反应在小波基下的动力可靠性分析世界地震动工程.2002,18(l):27-33页
[82]胡太彬，陈建军，王小兵．随机参数刚架结构的平稳随机位移响应动力可靠性分析．机械强度.2005,27(5):590-593页
[83]胡太彬，陈建军，王小兵，黄居峰．随机参数结构系统特征对的随机性及其关系分析．中国机械工程.2005,16(16):1427-1430页
[84]李桂青,曹宏,李秋胜,霍达.结构动力可靠性理论及其应用.地震出版社,1993:152-180页
[85]管昌生．张鹏，刘增夕，李桂青，李国发．时变结构动力可靠性分析的包络过程法．广西工学院学报.1995,6(3):25-30页
[86]黄继汤.空化与空蚀原理及应用.清华大学出版社，1991:1-2页，58-61页
[87] Stinebring D P, Billet M L, Lindau J W, ed. Developed Cavitation-Cavity Dynamics.VKI Special Course on Supercavitating Flows. Brussels.February.12-16,2001.Brussels: RTO-AVT and VKI,2001:67-95P
[88]傅慧萍,鲁伟敬,冯学梅.超空泡武器技术中的几个水动力学问题.船舶力学.2003,7(5):112-118页
[89] Munzer H, Reichardt H. Rotational symmetric source-sink bodies with predominantlyconstant pressure distributions [sic], ARE Translation1/50, Aerospace ResearchEstablishment, England,(as described in May,1975).
[90] Logvinovich G V. Hydrodynamics of Free-Boundary Flow, Tech. rep., U.S.Department of Commerce, Washington, DC,1972, translated from theRussian(NASA-TT-F-658).
[91] Vasin A D. The Principle of Independence of the Cavity Sections Expansion(Logvinovich's Principle) as the Basis for Investigation on Cavitation Flows, RTOAVT lecture series on supercavitating flows, Von Karman Institute, Brussels Belgium,February2001.
[92] Dzielski J, Kurdila A. A Benchmark Control Problem for Supercavitating Vehiclesand an Initial Investigation of Solutions, Journal of Vibration and Control, Vol.9,2003,791-804P
[93] Knapp R T, Daily J W, Hammitt F G. Cavitation. McGraw-Hill, New-York,1970.
[94] Logvinovich G V, Yakimov Yu L. High velocity entry of body into a liquid. In book:Non-Steady Flow of Water at High Speeds. Proc. of the IUTAM Symposium inLeningrad1971, Nauka Publishing House,1973
[95] Logvinivich G V. Hydrodynamics of Flows with Free Boundaries. English translation,New York: Halsted Press,1973.
[96] Garabedian P. Calculation of axially symmetric cavities and jets. Pac. Math.,1956,(4):611-684P
[97] Bodner V A. Aircraft control systems. Mashinostroeniye Publishing House. Moscow,1973
[98] Logvinivich G V. Some questions on planing.Trudy TsAGI1980，2052：3-12P
[99] Putilin S I. Stability of supercavitating slender body during water entry and underwatermotion.High Speed Body Motion in Water (AGARD Report827). Proc. FluidDynamics Panel Workshop.Kiev,1997
[100] Kirschner I N. Results of selected experiments involving supercavitating flows.VKISpecial Course on Supercavitating Flows,2001:313-342P
[101] Bolotin V V. The dynamic stability of elastic systems.San Francisco: HoldenDay,1964.
[102]马洪波,陈建军,崔明涛.随机参数桁架结构的有限元与可靠性分析.西安电子科技大学学报.2003,30（1）：103-107页
[103] Bolotin V V. The Dynamic Stability of Elastic Systems, Holden-Day, San Francisco,1964.
[104]曹伟,魏英杰,韩万金,王聪,闵景新.超空泡航行体典型弹道特性仿真研究.哈尔滨工程大学学报.2010,31（3）：323-328页
[105]莫文辉.机械振动的随机有限元方法.固体力学学报.2009,30:318-323页
[106]林家浩,易平.线性随机结构的平稳随机响应.计算力学学报.2001,18(4):402-408页
[107]安伟光,朱卫兵,严心池.随机有限元法在不确定性分析中的应用.哈尔滨工程大学学报.2002,23(1):132-135页
[2] Savchenko Yu N, Semenenko V N, ed. Unsteady super-cavitated motion of bodies.International Journal of Fluid Mechanics Research,2000,27(1):109-137P
[3] Vasin A D. Application of the Slender Body Theory to Investigation of the DevelopedAxially Symmetric Cavitation Flows in a Subsonic Steam of Compressible Fluid.International Journal of Fluid Mechanics Research,2001,28(5):702-716P
[4] Semenenko V N. Calculation of Two-Dimensional Unsteady Supercavities atArbitrary Time Dependence. International Journal of Fluid Mechanics Research,2004,31(6):621-632P
[5]袁绪龙,张宇文,王育才等.水下航行体通气超空泡非对称性研究.力学学报.2004,36(2):146-150页
[6]贾力平,于开平,张嘉钟,王聪等.空化器参数对空泡形成和发展的影响.力学学报.2007,39(2):210-216页
[7] Foote J P, Lineberry J T. Investigation of aluminum particle combustion forunderwater propulsion applications.ASME/SAE/ASEE,32nd Joint PropulsionConference and Exhibit, Lake Buena Vista, FL, July1-3,1996．
[8]田维平,蔡体敏,陆贺建,高波.水冲压发动机热力计算．固体火箭技术.2006,29(2):95-98页
[9]郜冶，贺征，刘平安．超空泡推进发动机燃料能量特性比较．固体火箭技术．2009，32(1)：27-32页
[10] Ruzzene M, Kamada R,ed. Trajectory Optimization Strategies for SupercavitatingUnderwater Vehicles. Journal of Vibration and Control,2008,14(5):611-644P
[11]冯光,颜开.超空泡航行体水下弹道的数值计算.船舶力学.2005,9(2):1-8页
[12]蒋运华,安伟光,安海.初始扰动下水下超高速运动体弹道数值模拟.水动力学研究与进展.2008,23(5):571-579页
[13] Dzielski J, Kurdila A. A Benchmark Control Problem for Supercavitating Vehicles andan Initial Investigation of Solutions. Journal of Vibration and Control,2003,9(7):791-804P
[14]魏英杰,王京华,张嘉钟等.水下超空泡航行体非线性动力学与控制.振动与冲击.2009,28(6):179-204页
[15]赵新华,孙尧,莫宏伟,李雪莲.水下超高速航行体纵向运动的控制方法研究.工程力学.2009,26(2):242-256页
[16] Vasin A D. Some Problems of Supersonic Cavitation Flows. In: Proceeding of the4thInternational Symposium on Cavitation, Pasadena CA,20-23June2001:1-13P
[17] Ruzzene M. Dynamic buckling of periodically stiffened shells: application tosupercavitating vehicles. International Journal of Solids and Structures,2004(41):1039-1059P
[18] Ruzzene M. Non-axisymmetric buckling of stiffened supercavitating shells: static anddynamic analysis. Computers&Structures,2004(82):257-269P
[19] Ruzzene M, Soranna F. Impact Dynamics of Elastic Stiffened Supercavitatingunderwater Vehicles. Journal of Vibration and Control,2004(10):243-267P
[20] Ahn S S, Ruzzene M. Optimal design of cylindrical shells for enhanced bucklingstability: Application to supercavitating underwater vehicles. Finite Elements inanalysis and design,2006(42):967-976P
[21] Choi J Y, Ruzzene M. Stability analysis of supercavitating underwater vehicles withadaptive cavitator. International Journal of Mechanical Sciences,2006(48):1360-1370P
[22] Alyanak Edward, Venkayya Vipperla, ed. Structural response and optimization of asupercavitating torpedo. Finite Elements Analysis,2005(6):563-582P
[23] Alyanak Edward, Venkayya Vipperla, ed. Structural response of a supercavitatingtorpedo shell.45th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics&Materials Conference,19-22April2004:1-8P
[24] Alyanak Edward, Venkayya Vipperla, ed. Variable shape cavitator design for asupercavitating torpedo.10th AIAA/ISSMO Multidisciplinary Analysis andOptimization Conference,30August-1September2004:1-26P
[25] Alyanak Edward, Grandhi Ramana, ed. Optimum design of a supercavitating torpedoconsidering overall size, shape, and structural configuration. International Journal ofSolids and Structures,2006(43):642-657P
[26] Choi J H, Penmetsa R C, ed. Shape optimization of the cavitator for a supercavitatingtorpedo. Struct Multidisc Optim,2005(29):159~167P.
[27] Edward Alyanak, ed. Cavitator Design for a Supercavitating Torpedo using EvidenceTheory for Reliability Estimation. Multidisciplinary Design Optimization for HighReliability and Robustness,2006:42-50P
[28]杨传武,王安稳.超空泡水下航行体振动特性分析.海军工程大学学报.2008,20(4):12-14页
[29]杨传武,王安稳.动态轴向载荷对超空泡航行体振动特性的影响.华中科技大学学报.2008,36(12):71-74页
[30]杨传武,刘刚,王安稳.超空泡体结构响应问题的有限元分析.海军工程大学学报.2008,20(2):101-104页
[31]杨传武,王安稳.冲击载荷作用下超空泡水下航行体的结构响应.华中科技大学学报.2008,36(7):129-132页
[32] Guang-ping Tian, Wei-guang An, Ling Zhou. Structure reliability analysis based onsupercavity vehicle steady motion. Journal of Harbin Institute of Technology (NewSeries),2009,16(2):251-254P
[33]麻震宇，胡凡，陈广南，张为华.超空泡航行体双层壳结构动力稳定性分析.国防科技大学学报.2011,33（4）：43-47页
[34]张劲生，张嘉钟，王聪，魏英杰.超空泡射弹结构响应的流固耦合仿真研究.船舶力学.2011,15（7）：763-768页
[35]张劲生，张嘉钟，魏英杰，王聪.超空泡射弹尾部冲击载荷的仿真研究.哈尔滨工业大学学报.2011,43（7）:19-22页
[36]张劲生,张嘉钟，魏英杰，曹伟.超空泡水下航行体的结构动力响应特性.北京航空航天大学学报.2010,36(4):411-414页
[37]孟庆昌,张志宏,顾建农,刘巨斌.超空泡射弹尾拍分析与计算.爆炸与冲击.2009,29（1）：56-60页
[38]顾永维,安伟光,安海.水下高速运动体的抗弯稳定可靠性分析.哈尔滨工程大学学报.2008,29(7):683-686页
[39]安伟光,顾永维,安海.初偏心影响下的水下高速运动体的抗弯稳定性及可靠性分析.兵工学报.2008,29(7):824-828页
[40]周凌,安伟光,安海.超空泡运动体强度与稳定性的非概率可靠性分析.哈尔滨工程大学学报.2009,30(4):362-367页
[41]周凌，安伟光，蒋运华，贾宏光.超空泡运动体圆柱薄壳屈曲可靠性分析.船舶力学.2011,15（7）：769-775页
[42] Wei-guang AN, Ling ZHOU, Hai AN. Structure buckling and non-probabilisticreliability analysis of supercavitating vehicles. Journal of Harbin Institute ofTechnology (New Series),2009,16(4):561-569P
[43]施连会,王安稳.轴向载荷下超空泡航行体动力稳定性的数值研究.振动与冲击.2011,30(2):55-59页
[44] Coodier J N, Dynamic Plastic Buckling in Dynamic Stability of Structure. ByHermann, G.1967:189-211P
[45] Gilat R, Feldman E.and Abordi J. Axisymmetric response of nonlinearly elasticcylindrical shells to dynamic axial laods, int.J. Impact Eng.,1993,13(4):545-554P
[46] Thomas J, Abbas B A H. Dynamic Stability of Timoshenk beams by Finite ElementMethod. Journal of Engineering for Industry,1976:1145-1149P
[47] Gurkan Sakar, Mustafa Sabuncu. Buckling and dynamic stability of a rotatingpretwisted asymmetric cross-section blade subjected to an axial periodic force. FiniteElements in Analysis and Design,2004:1399-1415P
[48] Briseghella L, Majorana C E, Pellegrino C. Dynamic stability of elastic structures: afinite element approach. Computers and Structures,1998:11-25P
[49] Movchan A A. The direct method of Liapunov in stability problems of elastic systems.J Appl Mach.1959,23:670-686P
[50] Movchan A A. Stability of processes with respect to two metrics. J Appl Mach Mech.1959,24:1506-1524P
[51] Leipholz H. Stability of Elastic Systems. Amsterdam: Leyden Noordhoff,1980:1-20P
[52] Budiansky B, Roth R S. Axisymmetric dynamic buckling of clamped shallow.NASA-TN-1510,1962:597-609P
[53] Hsu C S. On dynamic stability of elastic bodies with prescribed initial condition. Int JEng Sci,1966,4:1-21P
[54] Hsu C S. Stability of shallow Arches Against Snap-Through under Timewise Steploads. JAM,1968,35:31-39P
[55] Johnson E R, Mcivor I K. The effect of spatial distribution on dynamic snap-through.JAM,1987,45:612-618P
[56] Akkas N. Asymmetric buckling behavior of spherical caps under uniform step Pressure.JAM,1972,39:293-294P
[57] Butter T A, Baker W E, Babcock C D. Structural dynamics. Impact and Vibrat ion,Bulltion:1986:157-165P
[58] Goodier J N. Dynamic plastic buckling. In: Herrmann G ed. Dynamic stability ofstructure,1967:189-211P
[59]孙强，张本福.直杆的动力稳定性分析（Ⅰ）.安徽建筑工业学院学报.1996,4（1）：38-43页
[60]孙强，张本福.直杆的动力稳定性分析（Ⅱ）.安徽建筑工业学院学报.1996,4（2）：14-18页
[61]孙强，张本福.直杆的动力稳定性分析（Ⅲ）.安徽建筑工业学院学报.1996,4（3）：46-49页
[62]孙强.不同截面形状和材料柱的动力稳定性研究.工业建筑.2004,34(3):46-53页
[63]戴保东,郭秀峰,梁贵义.初弯曲对杆件动力性能的影响.山西机械.2000,3:37-38页
[64]曲淑英.大型空间框架结构的动力稳定性分析.世界地震工程.1998,14(3):44-48页
[65]李杰,郑凯锋.考虑大挠度效应及初偏心的压杆稳定性分析.昆明理工大学学报.2005,30(4):59-62页
[66]于龙文,杨乃山,陆阳南.考虑剪切影响时结构的动力稳定分析.抚顺石油学院学报.1996,16(1):27-32页
[67]童乐为，周国梁.偏心周期荷载作用下闭口薄壁构件的动力稳定性.上海力学.1992,12（2）：41-48页
[68]杨平,孙兰.偏心周期载荷作用下薄壁构件的动力稳定性.武汉交通科技大学学报.1998,22(4):403-407页
[69]杜文风,高博青,董石麟,谢忠良.一种判定杆系结构动力稳定的新方法——应力变化率法.浙江大学学报.2006,40(3):506-509页
[70]陆阳南.在纵向共振下结构的横向动力稳定分析.大连水产学院学报.1997,12(2):49-57页
[71]冯志华,胡海岩.轴向基础窄带随机激励柔性梁的稳定性与Hopf分岔.振动工程学报.2006,19(2):150-155页
[72]冯志华,芮延年,朱晓东,兰向军,张炜.轴向基础窄带随机激励悬臂梁的稳定性.动力学与控制学报.2004,2(2):74-78页
[73]高伟，陈建军，刘伟.随机参数智能桁架结构动力特性分析.应用力学学报.2003,20(l):123-127页
[74]戴君，陈建军，马洪波，崔明涛.随机参数结构在随机和在激励下的动力响应分析.工程力学.2002,19(3):64-68页
[75]高伟,陈建军.线性随机结构的平稳随机响应分析,应用力学学报.2003，20(3):92-95页
[76]欧进萍，王光远．结构随机振动.第一版．高等教育出版社，1998：347-359页
[77]朱位秋．随机振动．第一版．科学出版社，1992：249-369页
[78]李创第．李桂青，黄任常．连续随机结构的动力反应和可靠性分析．广西工学院学报.1997,8(l):25-31页
[79]石少卿．姜节胜.非平稳随机激励作用下多自由度体系系统动力可靠性研究应用力学学报.1999,16(4)：73-77页
[80]郑忠双．结构随机响应分析及其动力可靠性研究现状及趋势．福建建筑.2002,76(l):25-28页
[81]肖梅玲，高春涛，叶燎原．结构地震反应在小波基下的动力可靠性分析世界地震动工程.2002,18(l):27-33页
[82]胡太彬，陈建军，王小兵．随机参数刚架结构的平稳随机位移响应动力可靠性分析．机械强度.2005,27(5):590-593页
[83]胡太彬，陈建军，王小兵，黄居峰．随机参数结构系统特征对的随机性及其关系分析．中国机械工程.2005,16(16):1427-1430页
[84]李桂青,曹宏,李秋胜,霍达.结构动力可靠性理论及其应用.地震出版社,1993:152-180页
[85]管昌生．张鹏，刘增夕，李桂青，李国发．时变结构动力可靠性分析的包络过程法．广西工学院学报.1995,6(3):25-30页
[86]黄继汤.空化与空蚀原理及应用.清华大学出版社，1991:1-2页，58-61页
[87] Stinebring D P, Billet M L, Lindau J W, ed. Developed Cavitation-Cavity Dynamics.VKI Special Course on Supercavitating Flows. Brussels.February.12-16,2001.Brussels: RTO-AVT and VKI,2001:67-95P
[88]傅慧萍,鲁伟敬,冯学梅.超空泡武器技术中的几个水动力学问题.船舶力学.2003,7(5):112-118页
[89] Munzer H, Reichardt H. Rotational symmetric source-sink bodies with predominantlyconstant pressure distributions [sic], ARE Translation1/50, Aerospace ResearchEstablishment, England,(as described in May,1975).
[90] Logvinovich G V. Hydrodynamics of Free-Boundary Flow, Tech. rep., U.S.Department of Commerce, Washington, DC,1972, translated from theRussian(NASA-TT-F-658).
[91] Vasin A D. The Principle of Independence of the Cavity Sections Expansion(Logvinovich's Principle) as the Basis for Investigation on Cavitation Flows, RTOAVT lecture series on supercavitating flows, Von Karman Institute, Brussels Belgium,February2001.
[92] Dzielski J, Kurdila A. A Benchmark Control Problem for Supercavitating Vehiclesand an Initial Investigation of Solutions, Journal of Vibration and Control, Vol.9,2003,791-804P
[93] Knapp R T, Daily J W, Hammitt F G. Cavitation. McGraw-Hill, New-York,1970.
[94] Logvinovich G V, Yakimov Yu L. High velocity entry of body into a liquid. In book:Non-Steady Flow of Water at High Speeds. Proc. of the IUTAM Symposium inLeningrad1971, Nauka Publishing House,1973
[95] Logvinivich G V. Hydrodynamics of Flows with Free Boundaries. English translation,New York: Halsted Press,1973.
[96] Garabedian P. Calculation of axially symmetric cavities and jets. Pac. Math.,1956,(4):611-684P
[97] Bodner V A. Aircraft control systems. Mashinostroeniye Publishing House. Moscow,1973
[98] Logvinivich G V. Some questions on planing.Trudy TsAGI1980，2052：3-12P
[99] Putilin S I. Stability of supercavitating slender body during water entry and underwatermotion.High Speed Body Motion in Water (AGARD Report827). Proc. FluidDynamics Panel Workshop.Kiev,1997
[100] Kirschner I N. Results of selected experiments involving supercavitating flows.VKISpecial Course on Supercavitating Flows,2001:313-342P
[101] Bolotin V V. The dynamic stability of elastic systems.San Francisco: HoldenDay,1964.
[102]马洪波,陈建军,崔明涛.随机参数桁架结构的有限元与可靠性分析.西安电子科技大学学报.2003,30（1）：103-107页
[103] Bolotin V V. The Dynamic Stability of Elastic Systems, Holden-Day, San Francisco,1964.
[104]曹伟,魏英杰,韩万金,王聪,闵景新.超空泡航行体典型弹道特性仿真研究.哈尔滨工程大学学报.2010,31（3）：323-328页
[105]莫文辉.机械振动的随机有限元方法.固体力学学报.2009,30:318-323页
[106]林家浩,易平.线性随机结构的平稳随机响应.计算力学学报.2001,18(4):402-408页
[107]安伟光,朱卫兵,严心池.随机有限元法在不确定性分析中的应用.哈尔滨工程大学学报.2002,23(1):132-135页