Dynamic stability of a cracked pipe conveying fluid under thermal loads

Abstract

In the paper is investigated the effect of temperature load and crack position on the dynamic stability of a cracked straight pipe conveying fluid. The static scheme of the investigated pipe is a beam with restricted horizontal and vertical displacements at both of its ends. The velocity of the transported fluid is constant. The Galerkin method is applied for the solution of the differential equation of the transverse vibrations of the pipe. The differential equation is reduced to a first-order differential equation system. The system of differential equations is transformed and rewritten in a matrix form. The roots of the characteristic equation of the system are obtained by solving the generalized first order eigenvalue problem. A numerical solution for a cracked pipe conveying fluid with specified geometric and physical characteristics has been carried out. The temperature load, the position of the crack and the critical velocity of the fluid are considered as parameters of the problem. The results show that the temperature load and the crack position affect the vibrational characteristics of the pipe, as well as its critical velocity.