Flow-Induced Vibration of Pipeline on Elastic Support

Abstract

We study the self-excited flexural vibration of a pipe due to internal flow which is entirely supported on elastic foundation. We consider a finite length pipe with clamped ends made of isotropic material consist of an internal flow with constant velocity. The Euler-Bernoulli model of beam is considered to analysis the vibratory behavior of pipe. The governing equation of motion is then derived which is partial differential equation in terms of derivative of transverse displacement of pipe with respect to time and axial distance. The full term governing equation of motion contains the second derivative of transverse displacement with respect to time and axial distance which has been neglected in earlier work is considered here and solved analytically. The natural frequencies of coupled pipe-fluid system are then obtained and the effects of the neglected term on the natural frequencies of system are studied. The effects of the stiffness of elastic foundation, velocity and density of inner fluid, inner diameter of pipe with constant thickness, elasticity modulus of the pipe and finally pipe length are studied. The stability analysis of the vibration is also accomplished.