Nonlinear Dynamics of a Pipe Conveying Pulsatile Flow: Effect of an Asymmetric Spring Supported End

Flow-induced vibration of a fluid conveying pipe with a spring supported end is examined theoretically and experimentally under the condition that the fluid velocity has a small pulsatile component. The parametric resonance of the lateral pipe vibration is occurred due to the pulsating flow. In this paper, the four first-order ordinary differential equations, which govern the amplitudes and phases of the nonplanar pipe vibration, are derived from the nonlinear nonself-adjoint integro partial differential equations by the method of the Liapnov-Schmidt reduction. The effect of the asymmetric spring support on the nonlinear stability of the lateral pipe vibration is discussed with the obtained equations of amplitudes and phases. Furthermore, the experiments were conducted with the silicon rubber pipe conveying water. The lateral deflections of the pipe were measured by the image processing system, which was based on the images from two CCD cameras. The typical features of the parametric resonance were confirmed qualitatively.