The dynamic behaviors of the fluid-conveying pipes are the important information for the engineers, thus, the reports concerned are plenty. However, most studies are concentrated on the single-span pipes and the literature regarding the multi-span pipes is rare. In this paper, a fluid-conveying pipe with only the axial-loaded effect considered is called the “bare” pipe, and the one with all fluid-flow effects (including Coriolis force, damping forces, …) considered is called the “loaded” pipe, and the objective of this paper is to determine the first critical flow velocity of buckling and the corresponding buckled mode shape of the multi-span “loaded” pinned-pinned (P-P) pipe by using the analytical method and the finite element method (FEM). To this end, the analytical solution for free vibrations of the axial-loaded “bare” pipe is determined first, then the theory of mode superposition method is used to derive the equations of motion for the associated “loaded” pipe. Due to the effects of Coriolis force and the internal or external damping, the equations of motion of the “loaded” pipe take the form  and must be transformed into the other form  then some existing approaches can be used to solve the eigenproblem. In order to validate the results of the foregoing analytical method by those of FEM, the property matrices of a typical “loaded” pipe element are derived first, and then the standard assembly technique is used to construct the overall mass, damping and stiffness matrices for the equations of motion of the entire fluid-conveying “loaded” pipe so that one can obtained its damped (or un-damped) natural frequencies and mode shapes. For a “multi-span” P-P pipe with identical span lengths, it is found that its “first” dimensionless critical flow velocity leading to buckling is given by  with ndenoting the total number of spans for the entire “loaded” pipe, however, the last relationship is invalid if the span lengths are unequal. It is also seen that the numerical results of the analytical method and those of the FEM are in good agreement. Since the information relating to the dynamic characteristics of the “multi-span” fluid-conveying pipes is little, the presented approaches and results will be useful in the practical applications.

multi-span fluid-conveying pipe, analytical method, finite element method, Coriolis force, critical flow velocity.