The theory of thin shells is examined and some simplified general expressions are presented. These reduce to Donnell's expressions in the case of circular cylindrical shells. An appropriate variational principle is formulated and the similarity to shallow-shell theory is shown. These results and those of the more exact Flügge shell theory are applied to the problem of free vibration of conical shells. Approximate solutions are obtained by variational methods using the various theories and various displacement and stress functions. Comparison of the results indicates that the method which utilizes a logarithmic transformation of the axial coordinate in conjunction with appropriate dis¬placement expansion modes satisfying the geometrical boundary conditions yields results valid for both the membrane and bending cases and is capable of being used to obtain higher approximations. The results reveal that the influence of taper on membrane and bending frequencies of circular cyl¬inders is opposite in nature, the former being increased, the latter-decreased by the taper.
展开▼
