Application of Static Condensation Method to Vibration Analysis of Thin Cylindrical Shells

Abstract

A simple formula is proposed, by which the error in the natural frequencies introduced by using the static condensation method can be evaluated prior to the numerical computation, though its effective applicability is found in simple structures such as plates and shells. The effectiveness of the proposed formula is examined in the vibration analysis of thin cylindrical shells having freely supported ends by using various reduction patterns. Not only the accuracy of natural frequencies, but also that of modal displacements and the corresponding modal stresses are investigated by comparing with the results obtained without reduction and with the exact analytical solutions given by Arnold and Warburton.