NON-LINEAR DYNAMIC ANALYSIS OF ORTHOTROPIC OPEN AND CLOSED CYLINDRICAL SHELLS SUBJECTED TO A FLOWING FLUID

摘要

A theory is presented to predict the influence of nonlinearitiesassociated with the wall of the shell and with thefluid flow on the dynamic of elastic, thin, orthotropic openand closed cylindrical shells submerged and subjected to aninternal and external fluid. The open shells are assumed tobe freely simply-supported along their curved edges and tohave arbitrary straight edge boundary conditions. Themethod developed is a hybrid of thin shell theory, fluidtheory and the finite element method. The solution isdivided into four parts. In part one, the displacementfunctions are obtained from Sanders' linear shell theory andthe mass and linear stiffness matrices for the empty shell areobtained by the finite element procedure. In part two, themodal coefficients derived from the Sanders-Koiter non-linear theory of thin shells are obtained for thesedisplacement functions. Expressions for the second andthird order non-linear stiffness matrices of the empty shellare then determined through the finite element method. Inpart three a fluid finite element is developed, the modelrequires the use of a linear operator for the velocity potentialand a linear boundary condition of impermeability.With the non-linear dynamic pressure, we develop in thefourth part three non-linear matrices for the fluid. The non-linear equation of motion is then solved by the fourth-order Runge-Kutta numerical method. The linear and non-linearnatural frequency variations are determined as a function ofshell amplitudes for different cases.