Flow-induced vibration of ends-clamped curved pipe with the consideration of leakage and additional elastic support

To study the effects of leakage and additional elastic support on the fluid-structure interaction dynamics of ends-clamped curved pipe, on the basis of existed literature, its in-plane governing equation is obtained by introducing the added force generating from the elastic support and re-express the flow velocity, i.e. it's considered to be ideally changed by the leakage point in a step way at first, then a variable the output velocity dividing the input one is introduced to denote the decreasing ratio, finally, the flow velocity is formulated by a function of input velocity and a series of Heaviside functions. Galerkin method is used to derive the characteristic equation for calculating the system's natural frequencies. Parameters including added mass, viscous damping, decreasing ratio and leakage position, and coefficient as well as position of the elastic support are chosen as key researching objects in present study. After calculation, conclusions can be drawn that added mass and damping related to transverse motion take more responsibilities in decreasing natural frequencies than those in axial direction, different leakage positions may increase or decrease natural frequencies compared to without the consideration of leakage, all calculated modes will oscillate with the changing of position of the elastic support, their amplitudes and cycles are closely associated with elastic coefficient and order of mode. The present investigation lays foundations for further forced vibration analysis, and can also be radiated to study other types of fluid-structure interaction dynamic behaviors in other fields.