轴向周期载荷下超空泡射弹的动力稳定性分析
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摘要
针对超空泡射弹水下高速运动时前端受轴向载荷作用,建立超空泡射弹截锥形结构的动力偏微分方程,将其转化为二阶常微分Mathieu型参数振动方程,利用Bolotin方法对其动力稳定性进行数值计算,求解出动力不稳定区域边界.分别分析了不同弹体杆径比、不同射弹航行速度以及不同弹体长度等3种情况对超空泡射弹动力稳定性的影响.数值计算表明,当弹体杆径比增大时,射弹动力不稳定区域整体减小且不稳定激发频率增大;而弹体长度或航行速度增大时,射弹动力不稳定区域整体增大且不稳定激发频率减小.
The study takes aim at an examination of the axial load to the head of supercavitating projectile at high-speed motion underwater and builds the dynamic partial differential equation of supercavitating cut-off-cone structure.Secondly,the study examines the 2nd order ordinary differential Mathieu equation derived and the numerical calculation for the dynamic stability of supercavitating structure is conducted using the Bolotin method,thereby the boundary of dynamic instability area is derived.The influence of differences in rod diameter ratio,velocity and length of supercavitating projectile is analyzed to obtain the dynamic stability.The computational results indicate,with the increment of the rod diameter ratio,the regions of dynamic instability reduced and critical frequencies corresponding to dynamic instability ascended,while with the increment in velocity or length,regions of dynamic instability increscent and the critical frequencies corresponding to dynamic instability declined.
The study takes aim at an examination of the axial load to the head of supercavitating projectile at high-speed motion underwater and builds the dynamic partial differential equation of supercavitating cut-off-cone structure.Secondly,the study examines the 2nd order ordinary differential Mathieu equation derived and the numerical calculation for the dynamic stability of supercavitating structure is conducted using the Bolotin method,thereby the boundary of dynamic instability area is derived.The influence of differences in rod diameter ratio,velocity and length of supercavitating projectile is analyzed to obtain the dynamic stability.The computational results indicate,with the increment of the rod diameter ratio,the regions of dynamic instability reduced and critical frequencies corresponding to dynamic instability ascended,while with the increment in velocity or length,regions of dynamic instability increscent and the critical frequencies corresponding to dynamic instability declined.
引文
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[2]RUZZENE M.Dynamic buckling of periodically stiffened shells:application to supercavitating vehicles[J].International Journalof Solids and Structures,2004(41):1039-1059.
[3]AHN S S,RUZZENE M.Optimal design of cylindricalshells for enhanced buckling stability:application to super-cavitating underwater vehicles[J].Finite Elements in A-nalysis and Design,2006,42(11):967-976.
[4]CHOI J Y,RUZZENE M.Stability analysis of supercavitatingunderwater vehicles with adaptive cavitator[J].InternationalJournal of Mechanical Sciences,2006,48:1360-1370.
[5]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[J].哈尔滨工程大学学报,2008,29(7):683-686.GU Yongwei,AN Weiguang,AN Hai.Analyzing of buck-ling resistance of an underwater elastic body experiencinghigh speed motion[J].Journal of Harbin Engineering Uni-versity,2008,29(7):683-686.
[6]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[J].兵工学报,2008,29(7):824-828.AN Weiguang,GU Yongwei,AN Hai.Analysis of Anti-bending stability and reliability of an elastic body with initialeccentricity at high speed motion underwater[J].Acta Ar-mamentarii,2008,29(7):824-828.
[7]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[J].振动与冲击,2011,30(2):55-59.SHI Lianhui,WANG Anwen.Numerical study on dynamic sta-bility of supercavitation vehicles subjected to axial losds[J].Journal of Vibration and Shock,2011,30(2):55-59.
[8]孙强.杆桩结构的动力稳定与动力特性[M].合肥:合肥工业大学出版社,2005:58-59.
[9]BOLOTIN V V.The dynamic stability of elastic systems[M].San Francisco:Holden Day,1964:425-471.
[2]RUZZENE M.Dynamic buckling of periodically stiffened shells:application to supercavitating vehicles[J].International Journalof Solids and Structures,2004(41):1039-1059.
[3]AHN S S,RUZZENE M.Optimal design of cylindricalshells for enhanced buckling stability:application to super-cavitating underwater vehicles[J].Finite Elements in A-nalysis and Design,2006,42(11):967-976.
[4]CHOI J Y,RUZZENE M.Stability analysis of supercavitatingunderwater vehicles with adaptive cavitator[J].InternationalJournal of Mechanical Sciences,2006,48:1360-1370.
[5]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[J].哈尔滨工程大学学报,2008,29(7):683-686.GU Yongwei,AN Weiguang,AN Hai.Analyzing of buck-ling resistance of an underwater elastic body experiencinghigh speed motion[J].Journal of Harbin Engineering Uni-versity,2008,29(7):683-686.
[6]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[J].兵工学报,2008,29(7):824-828.AN Weiguang,GU Yongwei,AN Hai.Analysis of Anti-bending stability and reliability of an elastic body with initialeccentricity at high speed motion underwater[J].Acta Ar-mamentarii,2008,29(7):824-828.
[7]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[J].振动与冲击,2011,30(2):55-59.SHI Lianhui,WANG Anwen.Numerical study on dynamic sta-bility of supercavitation vehicles subjected to axial losds[J].Journal of Vibration and Shock,2011,30(2):55-59.
[8]孙强.杆桩结构的动力稳定与动力特性[M].合肥:合肥工业大学出版社,2005:58-59.
[9]BOLOTIN V V.The dynamic stability of elastic systems[M].San Francisco:Holden Day,1964:425-471.