An Approximate Method for the Determination of the Response Frequency of Pipe Whip

This paper is concerned with the effect of fluid flow on the static and dynamic characteristics of a simply supported pipe having a hole through the pipe wall to permit a fluid flow. In this approximate analysis based on the virtual work technique, system natural frequencies and mode shapes are determined and compared to the analytical solution of the linear problem given by G. W. Housner [3] and experimental solution of H. L. Dodds, Jr., and H. L. Runyan [2]. An approximate solution satisfying the initial and boundary conditions is presented for free vibrations and for steady-state forced vibrations for the nonlinear problem. In addition, the critical fluid velocity at which the system becomes statically unstable is verified.