流体管道横向振动的频域传递矩阵法

A transfer matrix method in frequency domain for lateral vibration of liquid-filled pipes

通过Fourier变换,把经典的时域描述的流体管道横向振动4方程模型变换到频域,求解此模型,可以得到单管的频域解析解。在此基础上,结合管段节点的平衡条件,推导出多管段的传递矩阵法,把单管的频域分析扩展到多管段组成的管路,传递矩阵法可以求解多管段的任意管段和任何坐标位置的值。最后,利用Dundee大学实验管道对结果进行验证分析,并通过算例来说明本方法的应用。

The classic equation model in time domain which describes the lateral vibration of fluid-filled pipes, was transformed into frequency domain by Fourier transformation. The analysis in this paper was undertaken directly in frequency domain, and an analytical solution in frequency domain of single pipe was obtained from the frequency-domain model. Then substituting the coordinate of the beginning and the end of the single pipe into the analytical solution and eliminating the constant vector, the transfer matrix of single pipe was obtaihed. Based on these, the transfer matrix method of pipe system was set up combined with the balanced boundary conditions, so the analysis of lateral vibration of single pipe was extended to pipe systems with multi-pipe sections. Using the method, the results of any coordinates of any pipe sections can be obtained. In the end, the results were validated by Dundee pipe, and two examples were presented to illustrate the application of the method.