Analysis of the nonlinear vibration of a clamped cylindrical shell considering the influence of the internal fluid and oceanic waves

Resumo

Cylindrical shells are used in various engineering installations, such as nuclear power plants, tanks,
cooling towers and oil platforms, which can fluid-filled. In addition, offshore structures are subject to the incidence
of ocean waves, which can change their dynamic response. Due to the slenderness of the cylindrical shells, the
interaction between these structures and the fluid presents a complex dynamic behavior, and understanding these
phenomena is of great interest for the development of these designs. This article presents an analytical-numerical
comparative study to analyze the nonlinear vibrations of a clamped cylindrical shell, considering the effects of the
presence of an internal fluid, that is incompressible, non-viscous and irrotational, and its free surface. It is also
applied to the outer side walls of the cylindrical shell, a load from the action of ocean waves, which are derived
from the Airy theory and are time dependent. To describe the deformation field and curvature changes of the
middle surface of the cylindrical shell, the nonlinear Sanders-Koiter theory was used. Chebyshev polynomials are

applied to define the modal expansions that describe the displacement field of the structure. Finally, the Rayleigh-
Ritz method is used to obtain the nonlinear equations of motion of the system. The free vibrations were compared

with a numerical model obtained by the Finite Element Method (FEM), with the aid of the commercial software
ANSYS. As a response of the nonlinear analysis, the response in time and phase-plane is obtained for the
cylindrical shell with the presence of the internal fluid and the action of ocean waves, in addition to evaluating the
influence of two types of waves, for shallow and intermediate waters.