Non-linear dynamic model of a fluid-conveying pipe undergoing overall motions

In this study, the investigation of the three-dimensional nonlinear dynamics of a fluid-conveying pipe undergoing overall motions is carried out. Considering the effect of the internal and external fluids, and using a non-Cartesian variable along with two Cartesian variables to describe the elastic deformation, the nonlinear differential equations are derived based on Kane’s equation in combination with the Ritz method. An alternative approach to the existing methods utilizing Newtonian balance equations or Hamilton’s principle is thus provided. The equations of motion are linearized in the neighborhood of the equilibrium position to implement the multimode linear stability analysis. In addition, the time histories for the displacements are obtained with the help of the Incremental Harmonic Balance (IHB) method. The validity of the new modelling is substantiated by comparing the model and results with those proposed by Païdoussis (1998).