3-D non-linear dynamics of inclined pipe conveying fluid, supported at both ends

Abstract In this paper, the three-dimensional (3-D) non-linear dynamics of inclined supported pipes conveying fluid with motion constraints are investigated. The motion constraints are modeled by an array of four and an array of two cubic non-linear springs. The spring forces are incorporated into the equations of motion via the method of virtual work. The equations of motion, obtained from Hamilton's principle, are discretized into 18 coupled non-linear ordinary differential equations using Galerkin's method, and solved numerically via Houbolts's method and Newton-Raphson iterative technique. Bifurcation diagram and oscillation trajectories are plotted to show the characteristics of some typical motions. The effect of system parameters, such as the inclination angel and spring stiffness, on the system dynamics is investigated.