Abstract
While the theories of vibrations of cylindrical shells have already been given by several authors, they are so complicated that very few cases have been solved actually, except such special cases that the displacement is in periodical from in both circumferential and longitudinal directions. When we are to deal with the vibration problems of cylindrical shell roofs, rather a simplified theory is often desired from the standpoint of practice since actually boundary conditions on the longitudinal edge are too involved to be dealt with mathematically. For this purpose of simplification approximate formulas are presented in this paper under some plain assumptions that only normal component of acceleration is taken into account whereas other components are neglected. Further, Zerna's approximations are also used. Then, the approximate theory thus obtained is applied to the cylindrical shell simply supported on stiffening walls which are rigid in their planes and flexible in the normal direction. Discussing the accuracy of this theory with the characteristic equation, we find this formula is applicable to the problem of shell vibration, if frequencies are low and shells are not extremely long. The frequency equation can be solved by trial method. As an example, the problem of free oscillations of shells are solved, whose longitudinal edges are free. On the other hand, experiments have been made and the results have been coompared with the above numerical example, showing good coincidence with respect to modes and frequencies. It will be said from these results that here presented approximate theory is sufficiently accurate to be used practically.
