基于实验设计和生死单元技术的时变质量杆件轴向振动问题研究

Study of Axial Vibration of Time-Varying Mass Rods Based on Experiment Design and Elements Birth and Death Method

关键词:  固体火箭  振动  时变质量  生死单元  实验设计  参数化  拉丁超立方

Key words:  Solid rocket  Vibration  Time varying mass  Element birth and death  Experiment design  Parameteric method  Latin hypercube sample method

摘要:

为研究固体火箭轴向振动问题，将火箭体系简化为时变质量轴向振动杆件。应用生死单元技术对时变质量杆件指定区域内均布质量的损失进行模拟。应用参数化方法将杆件的弹性模量及指定区域内均布质量线密度进行参数化，应用拉丁超立方抽样方法(LHS)及平面蒙特卡洛抽样方法(PMC)对时变质量杆件与恒定质量杆件的轴向振动问题进行2因素50水平实验设计，批量计算了不同工况下的杆件轴向振动响应。计算结果表明:基于实验设计和生死单元技术的参数化研究方法可以高效地对时变质量结构动力响应问题进行研究。应用LHS及PMC对杆件轴向振动问题进行研究时，可以得到与应用完备实验对杆件轴向振动问题进行研究时所得结论相类似的定性结论。部分工况下，恒定质量杆件的最大轴向振动响应明显小于时变质量杆件的最大轴向振动响应。依据恒定质量体系动力响应特性对箭体进行设计时，无法保证箭体及箭载设备的安全性。

Abstract:

In order to study the axial vibration of a solid rocket， a solid rocket system was simplified as a rod in axial vibration state. Mass reduction in a specific area of a rod in a time domain was simulated with the application of element birth and death method. Parameteric method was applied in the research to parameterize the elastic modulus and initial distributed mass density of rods. Latin Hypercube Sample method (LHS) and Plain Monte Carlo method (PMC) were applied in the experiment design of axial vibration problem of constant mass rods and time-varying mass rods with the density of initial distributed mass in the specific zone of rods and elastic modulus of rods as two factors. Each design had 50 levels， and the axial vibration of rods in different cases were calculated in batches. The results show that the dynamic response of time-varying mass rods can be investigated efficiently with the application of the parameteric method based on experiment design and element birth and death method. Similar qualitative conclusions can be drawn from the investigations of axial vibration of rods with the application of LHS， PMC and full sample experiment. Maximum axial vibration of constant mass rods are significantly lower than those of time-varying mass rods in some cases. Design of a rocket structure based on the characters of a constant mass system cannot guarantee the safety of the rocket and its facilities.