The fluid-structure interaction (FSI) can be observed significantly in the axial vibration of the liquid-filled pipe system. When distributed friction was neglected, the model could be solved with an exact solution without numerical error, developed from the method of characteristics (MOC). Then time-line interpolations have been employed to reduce the high time cost and retain the accuracy, named as the improved exact solution. For the purpose of practical applications, series connection of double-pipes is discussed in this paper. And complex constraints, including elastic, damping and inertial effects at connections, are studied. Models and methods are validated by numerical cases.

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