Vibration analysis of cylindrical shells by several finite difference schemes

Abstract

Several finite differencing schemes are used to compute the natural frequencies and mode shapes of simply supported circular cylindrical shells in an attempt to determine the most accurate numerical mode. Sets of difference equations are developed from the governing differential field equations and by minimizing the finite difference form of the Lagrangian energy function. Both finite differences and trigonometric expansions are used to model the circumferential behavior. Staggered or half-stations are used in addition to the conventional differencing schemes. The results indicate that the schemes using the trigonometric expansions are generally more accurate than those using finite differences for the circumferential derivatives. Furthermore, the conventional differencing scheme is shown to be as accurate as the half-station scheme when the field equation approach is used in conjunction with the trigonometric expansions