Simplified expressions for dynamic behavior of cylindrical shells uncoupled and coupled with liquids

Abstract

The dynamic behavior of cylindrical shells is essential in many practical applications. These include in-vacuum and coupled vibrations of structures with contained fluids. Closed-form solutions are extremely complex since they involve many terms and algebraic operations that require numerical solvers. In this work, a simplified closed-form solution for the free vibration analysis of an empty or filled with an inviscid and incompressible fluid cylindrical tank is presented. The proposed analytical method is developed for a simply supported cylindrical shell, based on an energy formulation obtained with variational calculus, and provides explicit expressions for natural frequencies, which can be easily programmed in a spreadsheet. The fluid is represented by an acoustic cavity, modeled by the wave equation, and the fluid-structure interaction is reduced to an added mass of fluid in the uncoupled shell equations of motion. A finite element model was built using ANSYS software to validate the proposed procedure. The natural frequencies and mode shapes were studied, and the results obtained are consistent with analytical, numerical and experimental results.

Nonlinear response of acid storage tank coupled with piping attachment under seismic load for optimal safe design

“…D. Oliveira França Júniora, P. Ribeirob, and L. Pedrosoa presented a simplified solution using analytical methods of the finite element method for calculations free vibration and dynamic analysis through Ansys software of empty and filled tank having incompressible and inviscid fluid (De Oliveira França Júniora, Ribeirob and Pedrosoa, 2019). S. Cherif and M. Ouissi proposed a quadrilateral hierarchical finite element constructed from the shifted Legendre orthogonal polynomials for the free vibration analysis of a liquid in a rigid cylindrical tank considering with or without a free surface (Cherif and Ouissi, 2016).…”