On the Vibration and Stability of Finitely Deformed Shallow Spherical Shells

Abstract

Equations describing the asymmetric vibrations of a shallow spherical shell which has suffered a finite axisymmetric displacement due to axisymmetric loading are studied by means of a finite-difference analysis. Results are obtained which show a continuous variation of the frequency spectrum as a function of the load parameter ranging from the previously computed frequencies and modes of the unloaded shell to the modes corresponding to vanishing frequencies which reveal the asymmetric buckling modes and loads for the shell. Excellent agreement with earlier work is found for both limiting cases thus providing an independent check on the asymmetric buckling loads recently computed by Huang.