Three-dimensional dynamics of a cantilevered pipe conveying pulsating fluid

This paper investigates the stability and three-dimensional (3-D) nonlinear dynamics of a cantilevered pipe with an internal fluid having a harmonic component of flow velocity su-perposed on a constant mean value. The nonlinear equations of motion for an inextensible cantilevered pipe with the consideration of internal pulsating flow are presented. The non-linear inertial terms in the governing equations are replaced by equivalent displacement and velocity terms by using a perturbation method. The partial differential equations are then transformed into a set of ordinary differential equations (ODEs) by using the Galerkin method. The instability regions of the subcritical and supercritical resonances of a linear system are determined via the Floquet theory. The effects of mean flow velocity and mass ratio are investigated. The resulting coupled nonlinear differential equations are numeri-cally solved using a fourth-order Runge-Kutta integration scheme for the subcritical and supercritical flow velocities. The nonlinear dynamical responses are presented in the form of bifurcation diagrams, time histories, phase portraits, power spectral densities (PSDs) and Poincare maps. Some interesting and sometimes unexpected results have been observed with different flow velocities. The analytical model is found to exhibit rich and variegated dynamical behaviors which include 2-D or 3-D periodic, quasiperiodic and chaotic motions. The convergence analysis of the number of truncating modes in the Galerkin approach is also conducted.(c) 2022 Elsevier Inc. All rights reserved.

Automated summary

This paper investigates the stability and three-dimensional nonlinear dynamics of a cantilevered pipe with internal fluid flow characterized by a harmonic component and a constant mean value. The research presents nonlinear equations of motion for the cantilevered pipe and uses numerical methods to analyze the resulting dynamical responses, revealing a rich variety of behaviors.