Nonlinear dynamic analysis of rotating pipe conveying fluid by the finite element method

Abstract

The rotating pipe conveying fluid is considered. Non-linear (geometrical non-linearity) equation of the motion of the pipe is derived using the finite element method. The equation of motion is derived based of the following assumptions: fluid is incompressible and inviscid; rotory inertia and shear deformation of the pipe are neglected. The sources of parametric vibration are: fluid velocity and pressure, angular speed of pipe. The possibility to solve a nonlinear response problem including sub-and/or super-harmonic using the finite element method is shown. Numerical results are derived considering the rotating cantilevered pipe conveying fluid. All matrices and vectors of the finite element method are derived by the symbolic computation system Maple.