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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 semi-analytical finite element method was used to establish the vibration equation, and decoupled and Fourier transformed. The deterministic dynamic stiffness expression was obtained. Taking into account the randomness of structural parameters, the Taylor expansion method and the random factor method were combined The random expression of dynamic stiffness, and discusses the effect of various random factors on the mean and coefficient of variation of dynamic stiffness. The calculated results show that the standard deviation of the stochastic factor of elastic modulus has the most prominent influence on the randomness of dynamic stiffness. When the other stochastic factors are unchanged and the standard deviation of stochastic factor of elastic modulus increases by one time, the dynamic stiffness of the three minimum points The average reduction ratio was 46.7%, and the mean values of dynamic stiffness decrease at 2 maximum points were 27.4% and 3.6% respectively. The variability of structural parameters was weak variability, and the variability of dynamic stiffness at the extreme point Then showed a moderate variation, even strong variation.