Finite element and differential quadrature solution for natural frequency of a clamped-free pipe conveying fluid

Abstract

The governing equation for the pipe conveying fluid is solved numerically using beam finite element and differential quadrature approach. It is well known that the governing equation for a pipe conveying fluids comprises of shear force due to bending, centripetal force, the force due to Coriolis acceleration, inertia force due to pipe and fluid mass. The detailed procedure on the differential quadrature method to solve the governing equation of the pipe conveying fluid has been outlined for finding out the natural frequency of pipe conveying fluid. Numerical exercises are presented for the vibration of pipe transporting fluid for the case of clamped-free pipe such that the transverse deflection at the clamped end is fully constrained however rotation of the normal is partially permitted. The error in the natural frequency obtained from the finite element and differential quadrature approach with respect to analytical solution ranges from 2.7 to 3.8%. � 2019 Author(s).