流体管道流固耦合14方程频域传递矩阵法

Frequency-domain Transfer Matrix Method of 14 Equations Model for Fluid-structure Interaction in Pipes

考虑流体管道的体积力以及流体的横向惯量,忽略管道和流体之间的摩擦效应,导出流体管道流固耦合的14方程模型。利用拉氏变换,把时域方程变换到频域,对频域模型进行推导,方程化为12个一元四阶常微分和2个一元二阶常微分,变换后的方程可以直接进行求解,得到简单直管的频域解析解。把管道始末端的坐标代入解析解,可得到管道始末端的关系,结合结点平衡条件,推导出多管段的频域传递矩阵法。对算例进行仿真计算和分析,并用实验结果来验证计算结果,验证模型和方法的正确性。

Based on the theory of beam model, a 14-equations model of fluid-structure interaction was set up, the volume force and lateral inertia of fluid was taken into account, but the friction between fluid and pipe was neglected. The time-domain model was transformed into frequency domain by Laplace transformation, and 12 fourth order ordinary differential equations and 2 second order ordinary differential equations was deduced. The equations can be solved directly to get the analytical solution in frequency domain of simple straight pipe. By the relation of the numerical results between the beginning and the end of the pipe, and combing with the boundary conditions, a transfer matrix of pipe system was gained. In the end, simulation was carried out, and the numerical results were verified by experimental ones.