Abstract
Spatial behavior of the pipe conveying fluid is examined theoretically and experimentally under the condition that the rotational symmetry is broken by the asymmetric spring supported end. When the flow velocity is over its critical value and has the small pulsating component, the interaction of the self-excited vibration and parametric excitaiton are occured. Four first-order ordinary differential equations, which govern the amplitudes and phases of the pipe vibration, are derived from the nonlinear nonself-adjoint partial differential equations by the liapnov-schmidt reduction. The planar motion, the beating and chaotic motions of the pipe vibration exist depending on the value of the pulsating frequency and the perturved parameter of the spring coefficient. Furthermore the experiments were conducted with the silicon rubber pipe conveying water. The spatial displacement of the pipe was measured by the image processing system which was based on the images from two CCD cameras.The typical feature of the pipe vibration,which has been predicted in the theory ,was confirmed qualitatively.
