Free vibration and stability analysis of a multi-span pipe conveying fluid using exact and variational iteration methods combined with transfer matrix method

In this paper, a new formulation based on the variational iteration method (VIM) is applied to investigate the dynamic behavior and stability of a multi-span pipe conveying fluid. Transfer matrix method (TMM) is used to assemble the system of equations resulting from applying the boundary conditions. The natural frequencies of the pipe system are obtained for different flow velocities. Results from VIM are compared with those predicted by the exact solution method and also with published literature. The influence of the number of spans on the VIM convergence is investigated. Also, the effects induced by varying the value and location of an intermediate elastic support on the critical velocity and stability are studied. It is shown that using VIM yields highly accurate results that are in very well agreement with the exact solution. The main advantage of the VIM is that it successfully overcomes well-known computational difficulties that are usually encountered during complex root finding step maintaining high precision as well.