传递矩阵法在计算输流管路高频振动时的稳定性改进

Stability improvement of the transfer matrix method when calculating the high requency vibration of a pipeline conveying fluid

传递矩阵法(transfer matrix method,TMM)是研究结构振动时常用的计算方法,但在计算大跨度输流管路高频横向振动时,TMM存在数值不稳定的现象,制约了其进一步应用。基于无量纲化计算结果得到的子单元划分准则的全局传递矩阵法(global transfer matrix method,GTMM)、混合能传递矩阵法(hybrid energy transfer matrix method,HETMM)和结合变精度算法的传递矩阵法(variable precision algorithm-transfer matrix method,VPA-TMM)等三种方法解决了这一问题。GTMM是最常用的TMM计算稳定性改进方法;HETMM系首次从层状介质中的波传播计算扩展到管路系统的振动分析领域,计算矩阵的维度和形式不随子单元数的变化而变化,计算时间最短;VPA-TMM无需进行子单元划分,可以看作是从根源上解决了TMM的长跨度高频计算失稳问题,但计算时间会大幅度增加。

The transfer matrix method(TMM)is a common calculation method for studying structural vibration,but it suffers from numerical instability in the high-frequency transverse vibration calculation of a large-span pipe conveying fluid,which limits its further application.The global transfer matrix method(GTMM)based on the subunit division criterion obtained from the dimensionless results,the hybrid energy transfer matrix method(HETMM)and the transfer matrix method combined with the variable precision algorithm-transfer matrix method(VPA-TMM)can solve this problem.Among these three methods,the GTMM is the most commonly used method to improve the stability of the TMM;the HETMM is extended from the calculation of wave propagation in layered media to the vibration analysis of pipeline system,the dimension and form of the HETMM calculation matrix do not change with the number of subunits,and the calculation time is the shortest;the VPA-TMM does not require subunit division,it can be seen as a solution to the TMM long-span high-frequency numerical instability problem from the root,but the computation time will increase significantly.