超空泡运动体结构的随机动刚度特性分析

Analysis of Random Dynamic Stiffness Characteristics of Supercavitating Vehicle Structure

采用半解析有限元法建立了振动方程,并对其进行解耦和傅里叶变换,得到了确定性动刚度表达式;考虑结构参数随机性,将泰勒展开法和随机因子法相结合,推导了动刚度的随机性表达式,并讨论了各种随机因素对动刚度均值和变异系数的影响。计算表明:弹性模量随机因子的标准差对动刚度随机性的影响最突出;其他随机因素不变,弹性模量随机因子的标准差增大1倍时,3个极小值点的动刚度均值减小比例均为46.7%,2个极大值点的动刚度均值减小的比例依次为27.4%、3.6%;结构参数的变异性为弱变异时,极值点的动刚度的变异性则表现为中等变异,甚至强变异。

The vibration equation is developed by semi-analytical finite element method. The mode-de- coupling and Fourier transform are used to deal with the vibration equation, and the expression of dynam- ic stiffness is obtained. Considering the randomness of structural parameters, the random expression of dynamic stiffness is deduced by Taylor expansion and the random factor method. The influences of ran- dom factors on the means and variation coefficient of dynamic stiffness are discussed. The calculation re- sults show that the standard deviation of elastic modulus random factor has a significant influence on the randomness of dynamic stiffness, and if all other factors are equal and the standard deviation of elastic modulus random factor is doubled, the decreasing ratios of all dynamic stiffness mean values in three minimum points are 46.7% , and are 27.4% and 3.6% for two maximum points in proper order Furthermore, when the variability of structural parameters belongs to week degree, the variability of dynamic stiffness in extreme points belong to moderate degree, even strong degree.