分支管流固耦合振动的频域解析解

Analytical solution in frequency domain to vibration in a branched pipe with fluid-structure interaction

利用拉氏变换,把时域流固耦合14方程模型变换到频域,对频域方程进行推导,得到12个一元四阶常微分方程和2个一元二阶常微分方程,对其求解,得到了直管的频域解析解。然后结合分支点的平衡条件以及分支管的边界条件,求解得出任意形状分支管的频域解析解。最后,对结果进行仿真计算,利用英国Dundee大学Tijsseling教授的实验结果对计算结果进行验证,并对不同形状的分支管进行了仿真计算。

The time-domain equation models describing axis vibration,lateral vibration and torsion vibration with fluid-structure interaction were transformed to ones in frequency domain using Laplace transformation,and twelve fourth-order ordinary differential equations and two second order ordinary differential equations were obtained.Solving those equations in frequency domain,an analytical solution in frequency domain to a single straight pipe was obtained.Then,with the equilibrium and boundary conditions of a branched point,the analytical solution in frequency domain was deduced for an arbitrary shape branched pipe.Finally,simulations were performed,the results were verified by test data made by professor Tijsseling in Dundee University of England.