Analysis of the instability of pipes conveying fluid resting on two-parameter elastic soil under different boundary conditions

In this study, the dynamic behaviour of a fluid conveying pipe resting on a two-parameter elastic foundation was investigated under four different boundary conditions. In the analyses, the fluid conveying pipe was modelled as an Euler-Bernoulli beam, and the equation of motion that describes the dynamic behaviour of the beam was obtained. The critical velocities and the complex frequencies of the system were obtained using the Differential Transform Method. The critical flow velocities and the corresponding instability forms that may induce pipe failure under four different boundary conditions were investigated in detail. The results of this study showed that the fluid conveying cantilevered and clamped-pinned pipes are more stable than the pinned-pinned pipe, but less stable than the clamped-clamped pipe; the elastic foundation increases the natural frequency and the critical fluid velocity, and induces stability of the pipe; it is easier for a fluid conveying pipe without elastic foundation to lose stability compared to a fluid conveying pipe resting on elastic foundation; increasing elastic foundation parameters increase the critical flow velocity and stability of the pipe, and delays the occurrence of divergence and flutter instabilities of the pipe.