Non-linear dynamics of cantilevered circular cylindrical shells with thickness stretch, containing quiescent fluid with small-amplitude sloshing

Studies on nonlinear vibrations of circular cylindrical shells containing fluid are mostly limited to thin simply supported shells, such that no results regarding the behavior of thick cantilevered shells with shear and thickness deformations can be found in the literature. In this article, for the first time, thin and thick circular cylindrical shells with clamped-free boundary conditions are modeled according to the third-order shear deformation theory with thickness stretch. The contained liquid satisfies the Laplace equation and linearized boundary conditions are imposed at the free surface and at the contact with the shell. Using Lagrange equations, the governing differential equations of the system in terms of shell-fluid interaction are derived. In linear free vibration analysis, it was found that increasing the fluid level inside the shell and decreasing the shell thickness, cause a significant rise in the fluid free-surface wave elevation. This increase is such that limits the application of linear sloshing theory. It was observed that the fluid presence can change the nonlinear behavior from softening to hardening type and intensifies the shell thickness deformation. In addition, the presence of contained liquid reduces the circumferential dynamic contraction of the shell caused by large amplitude vibrations.

Automated summary

Studies on nonlinear vibrations of circular cylindrical shells containing fluid have focused mostly on thin simply supported shells, leaving a lack of research on the behavior of thick cantilevered shells with shear and thickness deformations. This article presents, for the first time, models of thin and thick circular cylindrical shells with clamped-free boundary conditions based on the third-order shear deformation theory with thickness stretch. The derived governing differential equations describe the shell-fluid interaction. Results show that increasing the fluid level and decreasing the shell thickness in linear free vibration analysis significantly raise the fluid free-surface wave elevation, limiting the application of linear sloshing theory. The presence of the fluid changes the nonlinear behavior from softening to hardening, and intensifies the shell thickness deformation. Additionally, the contained liquid reduces the circumferential dynamic contraction caused by large amplitude vibrations.