列车荷载下土体时程反应的Ritz向量叠加法

Ritz vector superposition method for time-history analysis of soil under train load

针对轨道交通引起的土体振动计算存在耗时长的问题,为选择相对高效的方法进行场地动力反应分析,文章研究了基于Ritz向量叠加法的计算精度和计算效率。首先分析模态截断指标和土层位移反应峰值随向量阶数的变化规律,讨论不同模态截断指标的合理性;然后对比分析了Ritz向量叠加法、振型叠加法和直接积分法3种方法的计算效率。计算结果表明:基于动力贡献的截断指标与Ritz向量截断误差的变化规律相同,且基于模态截断指标所得向量数目略大于实际所需的向量数目,适合作为Ritz向量截断的依据;在计算精度基本相同的情况下,振型叠加法的计算耗时最长,直接积分法次之,Ritz向量叠加法最短。

The analysis of soil vibration caused by train load spends a lot of time normally.In order to select relatively efficient methods for site dynamic analysis,the calculation accuracy and computational efficiency based on Ritz vector superposition method were investigated.Firstly,the variation of modal truncation indexes and soil displacement responding with the quantity of vectors were analyzed,and the rationality of different truncation indexes was discussed.Then,the computational efficiency between Ritz vector superposition method,modal superposition method and direct integration method was compared.The results reveal that the truncation index based on dynamic contribution has the same trend of variation with truncation errors of Ritz vectors,and the quantity of vectors is slightly larger than actually needed,which is suitable to be a truncation index of Ritz vectors;the calculation time of modal superposition method is the longest,while the direct integration method takes a shorter one and the Ritz vector superposition method is the most efficient,under the same calculation accuracy.