管道系统时域响应的传递矩阵计算方法

基于输流管道数学模型，通过构造傅里叶级数展开形式的时域响应函数，对传递矩阵方法（TMM）求解的频响函数进行Laplace逆变换，实现管路系统的时域瞬态响应的计算；通过待定系数方法，基于TMM求解的简谐激励下的频响函数，求解管路系统的时域稳态响应，解决Laplace逆变换计算稳态响应不稳定的问题。最后以包含直管、弯管及弹性支撑的管路系统和悬臂梁为例，验证计算方法的正确性，与ANSYS的计算结果对比表明，所述的计算方法具有较高的精度，可用于管路系统时域响应的计算和分析。

Transfer Matrix Method for Analysis of Time-domain Response of Pipeline System

Based on the 12-equation model of fluid flow pipelines, constructing time-domain response functions by Fourier series expansion and applying the numerical inversion of Laplace transform to the transfer matrix method （TMM） for solution, the time-domain transient response simulation of pipelines is realized. The algorithm for solving time-domain steady response by undetermined coefficients method is employed, which can suppress the instability of the inverse Laplace transform in the solving process. To illustrate the practical implementation of the proposed methods, a pipeline system, which contains straight pipe, curved pipe, pipeline with elastic supports, and a cantilever pipe, is analyzed as an example, and the results are compared with those of finite element simulation. It is found that the results of proposed models and algorithm for the pipelines are close to the results of finite element simulation by means of ANSYS code. The feasibility of this method for solving the time-domain dynamics problems of the actual fluid-flow pipelines is validated.