Search

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. [ABSTRACT FROM AUTHOR]

Abstract In this paper, the coupled axial and transverse non-linear vibrations of a simply supported pipe, subjected to motion-limiting constraints, conveying pulsating fluid are investigated. The equations of motion are discretized into a set of coupled ordinary differential equations via Galerkin's method, which are then solved using Houbolt's method combined with Newton-Raphson iterative technique. The bifurcation diagrams are constructed to present the global dynamics of the system. Phase-plane portraits, Poincaré maps and power spectrum diagrams are plotted to show the characteristics of some typical motions, such as quasi-periodic and chaotic motions. Finally, the influence of axial motion on the system dynamics is investigated. [ABSTRACT FROM AUTHOR]