Abstract: Through analyzing the relationship between dimensionless complex frequency and critical flow velocity of cantilever pipe, the stability of cantilever pipe conveying fluid with distributed follower force on two-parameter elastic foundation was researched. The vibration of the cantilever pipe under actions of distributed follower force and flow velocity with four different values of foundation stiffness were also analyzed. On the basis of Euler-Bernoulli beam model, differential motion equations of pipes were established and the equations were solved by using transfer matrix method. Results show that 1) with given foundation stiffness, vibration characteristics of the cantilever pipes under the action of distributed follower force is obviously different from that of fluid velocity; 2) with given dimensionless distributed follower force and fluid velocity, the bigger foundation stiffness is, the more stable vibration condition of the pipes system is. In addition, the influence of shear stiffness is more obvious than that of linear stiffness.

Key words: two-parameter foundation, distributed follower force, cantilever pipes conveying fluid, foundation stiffness, dimensionless distribution