In-plane and out-of-plane motions of an extensible semi-circular pipe conveying fluid

In-plane and out-of-plane motions of a semi-circular pipe conveying fluid are analyzed in this paper. Assuming that the centerline of the semi-circular pipe is extensible, nonlinear equations of in-plane and out-of-plane motions are derived according to the extended Hamilton principle. The Lagrange nonlinear strain theory and the Euler–Bernoulli beam theory are used to derive the equations. The derived equations of motion are discretized by applying the Galerkin method. Linearized equations around the equilibrium position are obtained from the discretized equations, and then the dynamic characteristics of the pipe are investigated. In addition, some modelling issues, which are related to the nonlinearity of the circumferential strain and stress, are discussed. This study finds that a semi-circular pipe conveying fluid does not lose stability even at a high fluid velocity. Although a model using the Lagrange nonlinear strain and the corresponding nonlinear stress yields the most accurate computational results of the natural frequencies, a model using the Lagrange strain and a linearized stress is recommended to compute the natural frequencies efficiently while still maintaining accuracy.