Three-dimensional nonlinear vibrations of slightly curved cantilevered pipes conveying fluid

Abstract

In this paper, nonlinear static and dynamic behaviors of slightly curved cantilevered pipes conveying fluid under transverse base excitations are investigated. Incorporating geometrical and inertial nonlinearities, a new three-dimensional dynamic model is developed for the inextensible cantilevered pipe based on the Euler–Bernoulli beam theory. The resultant partial differential equations are discretized using the Galerkin method and solved utilizing the pseudo-arclength continuation technique and a time-integration method. The static equilibrium configuration, linear stability, and nonlinear response of the pipe are calculated for various cases, which allow us to investigate the effects of flow velocity, gravity coefficient, initial curvature amplitude and shape, and base-excitation amplitude and frequency. An emphasis is put on the importance of modal interactions on frequency-response and force-response relationships, evidencing the possible in-plane and out-of-plane transverse vibrations and identifying the preferred forms of pre- and post-instability behaviors. This study offers an efficient theoretical model for exploring the nonlinear forced response of slightly curved cantilevered pipes conveying fluid and provides a better insight for further investigations on the modal interaction in cantilevered pipe devices.