Nonlinear vibrations of cantilevered circular cylindrical shells partially filled with liquid presenting large-amplitude sloshing

Abstract

While fully numerical studies on nonlinear sloshing of liquids in various elastic and rigid containers exist, analytical studies on partially filled circular cylindrical elastic shells are limited to small-amplitude (linear) sloshing of the free liquid surface. In this study, for the first time, large-amplitude nonlinear vibrations of thin elastic shells, with clamped-free (cantilevered) boundary conditions, are coupled to large-amplitude sloshing liquid. The shell is modeled according to the Flügge-Lur’e-Byrne nonlinear shell theory. The liquid velocity potential satisfies the Laplace equation in the domain, and nonlinear boundary conditions are imposed at the free sloshing surface. Using the Lagrange multipliers method to satisfy the nonlinear boundary conditions for the liquid, the Lagrange equations of the system are made stationary. The effects of the liquid level inside the shell and nonlinearity at the free surface are investigated through frequency–response curves around resonances. It was observed that the sloshing nonlinearity often intensifies the softening behavior of the system in comparison to linear sloshing, and an increase in the liquid level inside the shell can have the same effect. Also, in contrast to some literature, it was found that there is a significant difference between considering nonlinear or linear sloshing during large amplitude vibrations of the shell, even when the free-surface oscillation amplitude is small.