On the Free Vibrations of Simply Supported Truncated Conical Shells

摘要

The problem of determining the bending natural frequencies and mode shapes of simply supported conical shells is investigated by a Rayleigh-Ritz solution of approximate equations of motion for the shell. Two types of simple support are considered, one for which edge circumferential displacements vanish, the other for which edge circumferential shear forces vanish. The differences between the two results are found to be quite significant when the circumferential wave number is small. Although a general explicit expression for the natural frequen cies of conical shells appears to be unobtainable, several approximations are illustrated and a simple expression for the minimum frequency is obtained. The results are in relatively good agreement with available experimental results. (Author)