Introduction

This chapter addresses the linear (small amplitude) and nonlinear (large amplitude) vibrations of circular cylindrical shells closed around the circumference (like a tube). Circular cylindrical shells are widely applied in aeronautical and aerospace engineering, in the petrol and chemical industry, in mechanical, civil, nuclear and naval engineering and in biomechanics. In fact, circular cylindrical shells are stiff structural elements that can be easily manufactured, for example, by folding and welding a metal sheet.

The linear vibrations of simply supported shells are studied by using the Donnell and the Flügge-Lur'e-Byrne theories. Fluid-structure interaction with still fluid is investigated. Numerical and experimental results are presented and compared.

The Rayleigh-Ritz method is introduced to study different boundary conditions and complicating effects, such as added masses and elastic bed.

The nonlinear vibrations of simply supported circular cylindrical shells under radial harmonic excitations are studied by using Donnell's nonlinear shallow-shell theory and the Galerkin method. For a periodic excitation applied to the circular cylindrical shell, a standing wave, symmetrical with respect to the point of application, is expected in the case of linear vibrations. This symmetrical standing wave is the driven mode. For large-amplitude vibrations, the response of the shell near resonance is given by circumferentially traveling waves, which can be in both directions (plus or minus θ). They can be described as the movement of the nodal lines of the driven mode.