Developing a Simplified Method to Investigate the Dynamic Behavior of Fluid Conveying Pipes under Mean Internal Pressure

Natural frequencies and critical velocities are the basic dynamic characteristics of fluid conveying pipes. Investigation of vibrations of fluid conveying pipes to control their dynamic behavior is one of the main topics of these structures. This paper presents a simplified approach to determine the natural frequencies and critical velocities of fluid conveying pipes with different typical boundary conditions under the mean internal pressure due to the fluid flow. The approach is suggested by reducing the order of mass, damping, and stiffness based on the concepts of the Galerkin method. The results of the method are validated by experimental results and compared with various numerical methods reported in the literature. The effects of mean internal pressure on the natural frequencies of fluid conveying pipes are assessed, and critical pressure values are calculated for the different mode shapes of the pipes. The method presents significantly better results in all the velocities in a range less than the critical flow velocity. Also, the natural frequencies of fluid conveying pipes in the presence and absence of mean internal pressure are calculated by the explicit formulas obtained by the simplified approach. The method has a lower computational cost than other more complex techniques, and its relative errors are less than 5%.