Vibration and stability analysis of functionally graded elliptical pipes conveying fluid with flow velocity profile modification

This paper aims to provide a new insight into the stability analysis of pipes/tubes conveying fluid with non-conventional cross sections that can be considered as an alternative design for traditional circular pipes used in a wide range of industrial applications. They provide the flexibility of being installed with major vertical or horizontal axes based on the desired hydraulic conditions and type of practical applications. However, the effects of non-uniformity of the flow velocity distribution need to be considered in the governing equations of pipes with non-conventional cross sections. In this paper, the influence of non-uniform flow velocity profile on dynamic behavior and instability of elliptical pipes made of functionally graded materials (FGMs) is studied. To achieve this goal, the traditional equation of motion for a circular pipe with an ideal fluid flow is modified through the recalculation of centrifugal and Coriolis forces for every differential element of the fluid. Timoshenko's beam theory is used to obtain the governing differential equations of motion and finite element method is utilized in the discretization process and solution of the governing equations of the problem. Consequently, critical flow velocities, divergence and re-stabilization behavior of the pipe are predicted using a modal analysis approach. The effects of power index and aspect ratio on the stability of FGM elliptical pipes are also investigated.

Automated summary

This paper investigates the influence of non-uniform flow velocity distribution on the dynamic behavior and instability of elliptical pipes made of functionally graded materials (FGMs) with non-conventional cross sections. The traditional equation of motion for a circular pipe is modified to consider the centrifugal and Coriolis forces, and the finite element method is used to discretize and solve the governing equations. The critical flow velocities, divergence, and re-stabilization behavior of the pipe are predicted using modal analysis. The effects of power index and aspect ratio on the stability of FGM elliptical pipes are also examined.