Analysis of vibration stability of fluid conveying pipe on the two-parameter foundation with elastic support boundary conditions

In this study, the vibration stability of fluid conveying pipe resting on two-parameter foundation is investigated under four different elastic support boundary conditions. The harmonic differential quadrature (HDQ) method is applied to solve the governing vibration equation derived based on Euler–Bernoulli beam theory subject to the elastic foundation and boundary conditions. As a result, a general set of second-order ordinary differential equations emerges, and by appropriately setting the stiffness of the end springs, one can easily study the dynamics of various systems with classical or non-classical boundary conditions. The numerical simulations are conducted to study the pipe instability performance with respect to various boundary conditions, elastic support parameters, elastic foundation parameters and fluid mass ratios. The numerical model is validated by comparison with published data. It is found that the elastic support boundary conditions have significant effects on the stability of pipe resting on elastic foundation. The pipe stability performance is very sensitive to the two elastic foundation parameters. Larger fluid mass ratio enhances the pipe flutter stability performance but has no effects on the divergence.