Stability of fluid conveying pipe on the two-parameter foundations with elastic support boundary conditions

In the report, the vibration stability of fluid conveying pipe under two-parameter foundations with elastic support boundary conditions was investigated. Based on the Euler-Bernoulli beam theory, the Hamiltonian principle was used to establish the dynamic equations of the pipe. The change of spring stiffness simplified the elastic support boundary conditions at both ends into various boundary conditions. The harmonic differential quadrature (HDQ) method was used to discrete and solve the vibration equations. The effects of the different spring stiffnesses, two parameter foundation parameters, and the fluid mass ratios on the critical velocity, critical frequency, and modal shape of the pipe were analyzed. The results indicated that the elastic foundation could effectively improve the stability of pipeline vibration. Additionally, the spring support and foundation had a significant effect on the vibration modes of the pipe.