Hybrid finite element analysis of large amplitude vibration of orthotropic open and closed cylindrical shells subjected to a flowing fluid Original Research Article

A hybrid finite element method is developed to predict the influence of large amplitude vibration of orthotropic, circumferentially non-uniform open and closed cylindrical shells submerged and subjected to an internal and/or external fluid flow. The open shells are assumed to be freely simply supported along their curved edges and to have arbitrary straight edge boundary conditions. The method developed is a combination of thin shell theory, fluid theory and the finite element method. The solution is divided into three parts. In part one, the displacement functions are obtained from Sanders’ linear shell theory and the mass and linear stiffness matrices for an open shell element are obtained by the finite element procedure. In part two, the modal coefficients, derived from the Sanders–Koiter non-linear theory of thin shells, are obtained for these displacement functions. Expressions for the second and third order non-linear stiffness matrices of the open shell element are then determined through the finite element method. With the dynamic pressure of the moving fluid and the boundary condition of impermeability, we develop in the third part the mass and the stiffness matrices of a fluid finite element for the interaction shell–fluid system. The non-linear equation of motion is then solved by the fourth-order Runge–Kutta numerical method. The linear and non-linear natural frequency variations are determined as a function of shell amplitudes for different cases. Here the uncoupled non-linear system is solved. The complete solution of the coupled non-linear system will be treated in a future work.