Finite element analysis of the vibratory characteristics of cylindrical shells conveying fluid

A finite element formulation is developed to predict the vibration of cylindrical shells conveying fluid. The method is based on the three-dimensional theory of elasticity and the linearised Eulerian equations. The hydrodynamic pressure is derived from the condition for dynamic coupling of the fluid–structure and the Eulerian equation. The influence of initial stresses within the shell due to fluid pressure is taken into account. Predicted natural frequencies for fluid–shell systems in the radius-to-thickness ratio range of R/ h=38.96–1624 are compared with published experimental results to validate the model, and are also compared with results obtained using other finite element models (based on the classical shell theory and potential flow theory) to demonstrate advantages and disadvantages in terms of accuracy. The effect of variation in flow velocities and hydrostatic pressures on the dynamic behaviour of fluid-conveying shells is examined, and the influence of supported conditions on the free vibration is also discussed.