超空泡运动体圆柱薄壳的非线性动力屈曲分析  

THE NONLINEAR DYNAMIC BUCKLING ANALYSIS OF A THIN-WALLED CYLINDRICAL SHELL OF SUPERCAVITATING VEHICLES

作　　者：王杰方[1,2] 安海[1] 安伟光[1] 

机构地区：[1]哈尔滨工程大学航天工程系,哈尔滨150001 [2]南昌工程学院土木与建筑工程学院,南昌330099

出　　处：《力学学报》2016年第1期181-191,共11页Chinese Journal of Theoretical and Applied Mechanics

基　　金：国家科技部国际合作专项资助项目(2012DFR00070)

摘　　要：超空泡运动体的动力屈曲失稳具有隐蔽性、突发性和危险性,因而必须研究清楚运动体的失稳区域边界及失稳振幅.将超空泡运动体模拟成受轴向周期载荷作用的细长圆柱薄壳,给出非线性几何方程、物理方程和平衡方程,建立细长圆柱薄壳带有非线性项的动力屈曲微分方程组;依据非线性项的形式,给出合理的非线性位移表达式,得到具有周期性系数的非线性横向振动微分方程;采用伽辽金变分法和和鲍洛金方法,获得带有周期性系数和非线性项的马奇耶方程;求解非线性马奇耶方程,得到第一、第二阶不稳定区域内的定态振动振幅的解析表达式;绘制超空泡运动体的非线性参数共振曲线,分析航行速度、载荷比例系数、轴向载荷频率和振型对参数共振曲线的影响.以上研究为建立基于参数共振的圆柱薄壳动力失稳的可靠性分析及基于参数共振可靠性的结构动力优化设计的奠定了理论基础.Dynamic buckling instability of the supercavitating vehicle has the characteristics of being hidden, sudden and dangerous. The researches of unstable region and instability amplitude are very important. The supercavitating vehicle was assumed as a thin-walled cylindrical shell with an axial periodic load. Considering the nonlinear geometric equation, physical equation and equilibrium equation, the nonlinear dynamic bulking differential equations were developed firstly, and then the nonlinear displacement expressions were given. After that, with the help of Galerkin variational method and Bolotin method, the dynamic bulking differential equation was transformed to Mathieu equation with periodic coefficients and nonlinear terms. At last, the nonlinear Mathieu equation was solved and the expressions of the stationary state vibration amplitude＇s in the 1 st order and the 2nd order unstable region were got. The nonlinear parametric resonance curves of supercavitating vehicle were obtained, and the influences of the speed, load ration coefficient, load frequency of axial load and the vibration mode to the resonance were analyzed. The researches laid theoretical foundation for the dynamic buckling reliability analysis based on parametric resonance of a thin-walled cylindrical shell and dynamic optimum design based on parametric resonance reliability.

关 键 词：超空泡运动体 圆柱薄壳 非线性 动力屈曲 参数共振 

分 类 号：O343.9[理学—固体力学]