The role of median surface curvature in large amplitude flexural vibrations of thin shells

General conclusions regarding the non-linear vibration of structural components like curved beams, rings and thin shells are derived from the study of two specific examples, the circular ring and shallow spherical shell. It is shown that whereas the non-linear behaviour of flat plates and straight bars is generally of a hardening type, the behaviour of thin structural elements that have a finite curvature of the undeformed median surface in one or both principal axis directions may be of the hardening or softening type, depending on the structural parameters as well as on whether the shell is open or closed. It is seen that with careful judgment in the use of mode shapes of one or more terms, the resulting modal equations help one to appreciate much better the physics of the problem, whereas sophisticated mathematical models tend to obscure this