Effect of rotary inertia of concentrated masses on the natural frequencies of fluid conveying pipes

Abstract

The effect of concentrated masses on the natural frequency variation of the fluid conveying pipes for the two boundary conditions of the simply-supported pipe and clamped-clamped pipe is studied by computer simulation and by experiment. Rotary inertia effect of the concentrated masses is accordingly included in the governing equation. In the computer simulation work, Galerkin``s method is used for transformation of the governing equation to the eigenvalue problem and the natural frequencies are found in all possible regions-stable, unstable, and neutral stable. In the experiment, the natural frequencies are found in the neutral stable region for the variations of the fluid velocity, the concentrated mass, and its location. Water is used as working fluid and polymethyl-methacrylate pipe is used as the fluid conveying pipe. Introduction of an even slight mass of concentration brings large variation of the natural frequency. The rotary inertia effect also changes the natural frequency very much, so that its neglect results in large error. The results of both computer simulations and experiments show that they are in the good agreement in the extent of about 10 percent error bound when the rotary inertia effect is included for our analysis. The effect of the rotary inertia of concentrated mass can change not only the natural frequency but also its unstable velocity at higher modes.