Dynamic behavior of a fluid conveying pipe subjected to a moving sprung mass – An FEM-state space approach

In this paper, the dynamic behavior of a pipe conveying fluid, with a sprung mass moving on it is studied. The governing equation is obtained in the transverse and longitudinal directions based on the nonlinear Von-Karman sense, by which large displacements may be taken into account. The effect of rotary inertia is also considered. Using the Galerkin method with appropriate shape functions, the dynamic equations are discretized spatially. In developing the equations of motion, a nonsymmetric damping matrix emerges due to the Coriolis effect. As a result, the eigen-values (damped natural frequencies) and eigen-vectors (mode shapes) are to be obtained by the state-space method. First, only the effect of fluid flow is considered, and the results obtained show good agreement with analytical ones under different fluid velocities. After validation of the results, the effect of a moving sprung mass with damping is added to the system, and using the Newmark-β integration scheme, the response of the system is obtained for different moving load and fluid velocities. The results show that moving mass changes the dynamic properties of the system on the one hand, and acts as an external source of force in the vibration the system on the other.