First, the sensitivity theory is introduced. Then, based on the one-dimensional wave equation, the frequency equation of the standard beam is obtained. According to the structure feature, the train car-body is divided into some parts to get their cross-sectional information. With the stiffness tandem principle and some related correction factor, first order torsional vibration frequency equation of car-body is obtained. Taking a car-body of high-speed train, for example, the error of analytical calculation result with the finite element result is-2.036%, which is within the error scope of engineering requirements. Finally, 8 set of design parameters are selected to do the sensitivity analysis based on the analytical formula, showing that 4 set of them can make great impact on the vibration frequency, which can give car-body designers some suggestions.%首先介绍了灵敏度分析的基本原理,然后基于一维波动方程,导出了标准梁的扭转振动频率方程,结合列车车体中空薄壁型腔截面的特点,根据不同位置的截面特性,将车体分成多段等截面梁,以获取不同车体分段的截面信息.运用刚度串联原理,引入与车体结构特征密切相关的修正系数,得到车体的一阶扭转振动频率方程.以某型高速列车为例,公式的解析计算结果与有限元结果的误差为-2.036%,在工程误差要求范围内.最后,以该解析公式为依据,选取了车体的8组设计参数对车体进行了灵敏度分析,并得到了对车体扭转振动频率影响较大的4组设计参数,为列车车体设计相关工作提供了设计参考依据.
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