抄録
In this paper, we examine the nonlinear lateral vibration of a flexible pipe with a spring supported end, which is parametrically excited due to a pulsating flow. Using Liapnov-schmidt reduction, two first-order ordinary differential equations, which express the amplitude and phase of the lateral pipe vibration, is derived from the nonlinear nonself-adjoint partial differential equation governing the lateral pipe vibration. A first order ordinary differential equation, which govern the dynamics on the center manifold around the pitchfork bifurcation is derived from the amplitude equations of the lateral pipe vibration, with use of the center manifold reduction method. As a result, we clarify the nonlinear effect of the spring supported end on the stability and the lateral displacement of the pipe, from the view point of qualitative nonlinear analysis.
