考虑流固耦合的多分支管道系统振动研究

利用拉普拉斯变换,把时域14方程模型变换到频域,并化多元一阶常微分方程为一元高阶方程,对其求解,得到直管的频域解析解。然后把任一管段的初始坐标值和末端坐标值代入直管的频域解析解,得到单管的传递矩阵,结合分支点的平衡条件,便可以推导出任意N个分支管的传递矩阵。增加7(N+2)个分支管的边界条件,求解得出任意N分支管路的频域解。最后,进行仿真计算,利用英国Dundee大学Tijsseling教授的实验结果以及ANSYS仿真计算对结果进行验证,验证了文中方法的正确性;并例举了不同分支数目以及不同分支位置管路的仿真计算结果,同时对仿真结果进行了分析。

Research on vibration of multi-branched pipe system considering fluid-structure interaction

The time-domain equations describing fluid-structure interaction,were transformed to frequency domain by Laplace transformation,and twelve fourth order ordinary differential equations and two second order ordinary differential equations were deduced.Solving the equations in frequency domain,an analyti-cal solution of single straight pipe was obtained.Then replacing the coordinate in the solution by the pipe ini-tial coordinates and the pipe end coordinates,the transfer matrix of single straight pipe can be deduced.With equilibrium conditions of the branched point,the transfer matrix of N branched pipes arbitrarily shape was obtained.Combing with 7(N+2) equations describing the branched pipe boundary conditions,an analytical solution of multi-branched pipe in frequency domain was obtained.Finally,simulation was carried out,and the results were verified by experiment carried out by professor Tijsseling in Dundee University of England and results from ANSYS simulation,the correctness of this method was validated;and different number and different position of branched pipes were presented here to illustrate the application of the method,and the simulation results were analyzed.