Semi-analytical solution for dynamic behavior of a fluid-conveying pipe with different boundary conditions

Abstract

This paper analyzes the dynamic behavior of a fluid-conveying pipe with different pipe end boundary conditions. The pipe is considered to be an Euler-Bernoulli beam, and a motion equation for the pipe is derived using Hamilton's principle. A semi-analytical method, which includes the differential quadrature method (DQM) and the Laplace transform and its inverse, is used to obtain a model for the dynamic behavior of the pipe. The use of DQM provides a solution in terms of pipe length whereas use of the Laplace transform and its inverse produce a solution in terms of time. An examination of the results of sampling pipe displacement at different numbers of sample points along the pipe length shows that the method we developed has a fast convergence rate. The frequency and critical velocity of the fluid-conveying pipe derived by DQM are exactly the same as the exact solution. The numerical results given by the model match well with the result obtained using the Galerkin method. The effect on pipe displacement of the pipe end boundary conditions is investigated, and it increases with an increase in the edge degrees of freedom. The results obtained in this paper can serve as benchmark data in further research.