Modeling and modal analysis of non-uniform multi-span oil-conveying pipes with elastic foundations and attachments

•Modal analysis for a non-uniform multi-span pipe with foundations and attachments.•A new Modified LTMM can deal with flow velocity and foundations is proposed.•A simple-formed governing equation with various boundary conditions is derived.•The effects of parameters on modal characteristics are discussed numerically. This paper studies the parametric modal characteristics of non-uniform multi-span oil-conveying pipes, considering many combined factors such as the various foundations that pipes rest on, the accessary masses attached to the pipes, and the flow moving inside the pipes. A new modified lumped-mass transfer matrix method (LTMM) is proposed to derive the governing equation of the system, where we simplified and modeled all the combined factors as lumped masses and springs that can be treated in uniform ways. The boundary is also modeled in a similar lumped-spring strategy. In such a way, the system with combined factors and various boundary conditions is eventually modeled as a “Free-Free” pipe with only lumped masses and springs. Numerical results are illustrated to testify the accuracy and efficiency of the proposed method, and a general case with combined factors affecting the modal characteristics is discussed. It can be presented that rotary inertia and concentrated mass can affect different order mode shapes; under different foundation parameters, the differences between mode shapes are remarkable while the positions of the nodes do not change much, even under classical boundary condition. The results through modal analysis can afford the basis for the vibration analysis, fault diagnosis and prediction, and the optimization design of the dynamic characteristics of the structure.