Stability and Vibration Analysis of Porous Axially Graded Pipe Conveying-Fluid Lying on Pasternak Foundation

This paper investigates the stability of an axially functionally graded (AFG) pipe carrying fluid flow supported by two elastic foundations and constrained by double-clamped end conditions.Hamilton's principle provides the vibration equations, while the Galerkin procedure discretizes the system equation to facilitate analysis of the dynamic behaviour.The pipe's mechanical properties vary along the axial direction according to a power-law distribution.The model incorporates the effects of different porosity, axial grading, fluid velocity, and foundation stiffness on the system's dynamic behaviour.Numerical results show that an increase in fluid velocity by 20% results in a 30% reduction in the first frequency, indicating enhanced system instability.Additionally, modules of elasticity ratio significantly influence the natural frequencies, with variations in gradient index leading to a 19% increase in the system's fundamental frequency.The Pasternak foundation provided a stabilizing effect, with a 20% increase in foundation stiffness, improving the stability margin by 25%.These findings show that porosity, axial grading, and foundation parameters play important roles in determining fluid-conveying pipes' vibration characteristics and stability.