Free vibration analysis of a clamped cylindrical shell with internal and external fluid interaction

Cylindrical shells filled with fluid are structures widely used in different engineering installations, such as oil platforms, nuclear power plants and storage tanks. In offshore structures, the action of ocean waves must be carefully evaluated, because the influence of the external fluid to the external walls of this structure can modify its dynamic behavior. This article presents an analytical-numerical approach to analyze the linear vibrations of a clamped cylindrical shell, considering the presence of external and internal fluid with the inclusion of the effects of the free surface motion of the internal fluid. The strain fields and curvature changes of the middle surface of the cylindrical shell are described by the Sanders–Koiter linear theory. The modal expansions, that describe the displacement fields of the clamped cylindrical shell, are obtained from the Chebyshev polynomials. Finally, the Rayleigh–Ritz method is used to derive the linear equations of motion of the system which, in their turn, are solved to obtain the natural frequencies and vibration modes of the clamped cylindrical shell with external and internal fluid interaction. The obtained results are compared, when it is possible, with others works found in the literature. Also, a finite element analysis in a commercial software is conducted to evaluate the reliability and the convergence of the obtained analytical-numerical results. They indicate that the fluid level alters the free vibrations of the cylindrical shell. The consideration of the external and internal fluid for free vibration analysis with application of a hydrodynamic pressures is important, since it incorporates additional mass and reduces the values of natural frequencies. The influence of the free surface also alters the free vibrations of the cylindrical shell, and for large structures, a considerable effect is observed that cannot be disregarded.