Vibration of pre-stressed thin cylindrical shells conveying fluid

A general approach to modelling the vibration of prestressed thin cylindrical shells conveying fluid is presented. The steady flow of fluid is described by the classical potential flow theory, and the motion of the shell is represented by Sanders' theory of thin shells. A strain-displacement relationship is deployed to derive the geometric stiffness matrix due to the initial stresses caused by hydrostatic pressure. Hydrodynamic pressure acting on the shell is developed through dynamic interfacial coupling conditions. The resulting equations governing the motion of the shell and fluid are solved by a finite element method. This model is subsequently used to investigate the small-vibration dynamic behaviour of prestressed thin cylindrical shells conveying fluid. It is validated by comparing the computed natural frequencies, within the linear region, with existing reported experimental results. The influence of initial tension, internal pressure, fluid flow velocity and the various geometric properties is also examined.