Flow-induced vibration of curved pipe conveying fluid by a new transfer matrix method

A new transfer matrix method based on the Laplace transform is proposed to analyze the flow-induced vibration of curved pipe conveying fluid. After the comparison with the existing literature, the proposed method is verified to be of high accuracy in calculating critical flowing velocity. Three examples including cantilevered, clamped-elastically supported, and periodic cantilevered curved pipes are investigated by the proposed method, natural frequency as a function of the flowing velocity for the former two cases and critical velocity for all of them are calculated not only to obtain some discoveries never mentioned in other literatures, but also to show its broad applications. For the first time, it is pointed out that the steady combined force should be considered in an appropriate interval during the calculation of clamped-elastically supported curved pipe. The method can also be radiated to study other forms of vibration problems concerning fluid conveying pipes or other problems characterized by the chain structure