Parametric resonance and suppression for L-shaped pipe conveying pulsating fluid

This work establishes a new dynamic model for solving parametric resonance and suppression of a L-shaped pipe conveying pulsating fluid, which can be extended to arbitrary pipe configurations. Firstly, the linear dynamic analysis for the L-shaped pipe conveying steady-state fluid is performed. The new results show that there are more wave numbers of the mode shape than those for the straight pipe. With increasing the flow velocity, the natural frequency is decreased and the mode shape is changed from symmetry to asymmetric characteristics. Subsequently, the nonlinear dynamic analysis is conducted for the L-shaped pipe conveying pulsating fluid. It is found that primary and subharmonic resonance behaviors are newly produced due to parametric excitations. At the same time, the subharmonic resonance occurs for the pipe to have much higher vibration amplitudes than the primary resonance. Finally, the strategy of adding an intermediate support is proposed to suppress vibrations of the L-shaped pipe conveying pulsating fluid. Results indicate that there is an optimal position for the L-shaped pipe to add the intermediate support, which can significantly reduce the vibration amplitude. This optimal position is exactly where the fundamental frequency of the pipe system is maximized.