Parametric resonance of pipes with soft and hard segments conveying pulsating fluids

In this paper, the parametric resonance of pipes with soft and hard segments induced by pulsating fluids is investigated. The lowest six natural frequencies and mode shapes of the soft-hard combination pipe simply supported at both ends are obtained by the modified Galerkin's method. The Floquet method is used to numerically determine the parametric resonance regions, including subharmonic resonance regions and combination resonance regions. The parametric resonance results are verified by comparison with published ones, which confirm the validity of the present model establishment and numerical calculation. Compared with a uniform pipe conveying fluid simply supported at both ends, the soft-hard pipe conveying fluid is found to reveal different dynamical behaviors. Decreasing the length of the soft pipe, while increasing the stiffness ratio of the hard pipe compared to the soft one, can effectively improve the stability of the pipe system. The parametric resonance results show that the mean flow velocity and pulsation amplitude of the fluid have a great influence on the width of the parametric resonance regions. It is advisable that the ratio (the soft pipe/the whole pipe) of the length may be designed to be 0.4-0.5 for a flexural rigidity ratio (the hard pipe/the soft pipe) of 2. As the stiffness ratio (the hard pipe/the soft pipe) increases beyond 26, the hard pipe may be regarded as a rigid pipe. The probability of parametric resonance occurrence will be smallest if the soft-hard combination pipe is supported in a clamped-pinned way. For certain application cases, the safety design length of the two pipes with different materials can be determined through numerical calculation.