Introduction

Nonlinear vibrations of simply supported circular cylindrical shells are studied in Chapters 5 and 7. However, shells can have different boundary conditions in practical applications.

In this chapter, the effect of boundary conditions on the nonlinear forced vibrations of circular cylindrical shells is investigated. Numerical results show that, for the case analyzed, the axial constraint largely increases the softening-type nonlinearity of the shell with respect to the simply supported shell. On the other end, for the studied thin shell, the effect of the rotational constraint is very small.

Literature review

Studies comparing the results for nonlinear vibrations of circular cylindrical shells with different constraints are very scarce. In fact, most of the literature deals with simply supported shells. Not many studies on shells with different boundary conditions are available. In particular, Matsuzaki and Kobayashi (1969) studied large-amplitude vibrations of clamped circular cylindrical shells theoretically and experimentally. They based their analysis on Donnell's nonlinear shallow-shell theory and used a simple mode expansion with two degrees of freedom (dofs). The analysis found a softening-type nonlinearity for clamped shells, in agreement with their own experimental results. They also found quasi-periodic response close to resonance.

Iu and Chia (1988) used Donnell's nonlinear shallow-shell theory to study free vibrations and post-buckling of clamped and simply supported, unsymmetrically laminated, cross-ply circular cylindrical shells. A multimode expansion was used without considering the companion mode, so that only free vibrations were investigated. Radial geometric imperfections were taken into account.