Natural vibrations of a pipeline segment

Abstract

Transverse natural vibrations of an extended segment of a pipeline conveying a uniformly moving fluid are studied. The mechanical model under study takes into account the pipe and fluid inertia forces and the moment of the Coriolis and centrifugal forces due to the medium motion. It is assumed that both ends are rigidly fixed and the elastic characteristics are constant along the pipe. A mathematical model is developed on the basis of a generalized procedure of separation of variables, and a boundary value problemfor the eigenvalues and eigenfunctions (natural frequencies and vibration shapes) is posed. Ferrari’s formulas are used to solve the fourth-order complex characteristic equation for the wave parameter, and a closed procedure of numerical-analytical determination of roots of the secular equation for the frequencies is obtained. The frequency curves for the firsts two vibration modes against the dimensionless velocity and inertia parameters are constructed. The forms of the observed motions at different times are obtained. Several effects are revealed indicating that there is a dramatic quantitative and qualitative difference between these vibrations and the standard vibrations corresponding to the case of immovablemedium. We discover the absence of a rectilinear configuration of the axis, the variable number and location of nodes, their inconsistency with the mode number, and some other effects.