On the Validity of Flat-Plate Finite Strip Approximation of Circular Cylindrical Shells

Abstract

The validity of modeling curved shell panels using flat-plate finite strips has been demonstrated in the past by comparing finite strip numerical results with analytical solutions of a few benchmark problems; to date, no mathematical exact solutions of the method or its explicit forms of error terms have been rigorously derived to demonstrate analytically its validity. Using a unitary transformation approach (abbreviated as the U-transformation herein), an attempt is made in this paper to derive mathematical exact solutions of flat-plate finite strips in cylindrical shell vibration analysis. Unlike the conventional finite strip method which involves assembly of the global system of matrix equation and its numerical solution, the U-transformation method makes use of the inherent cyclic symmetry of cylindrical shells to decouple the global matrix equation into one involving only a few unknowns, thus rendering explicit form of solutions for the flat-shell finite strip to be derived. Such explicit solutions can be subsequently expanded into Taylor's series whose results reveal directly their convergence to the exact solutions and the corresponding rate of convergence.