Effects of elastic foundation on the dynamic stability of cylindrical shells

A formulation for the dynamic stability analysis of cylindrical shells resting on elastic foundations is presented. In this previously not studied problem, a normal-mode expansion of the partial differential equations of motion, which includes the effects of the foundation as well as a harmonic axial loading, yields a system of Mathieu-Hill equations the stability of which is analyzed using Bolotin\'s method. The present study examines the effects of the elastic foundation on the instability regions of the cylindrical shell for the transverse, longitudinal and circumferential modes.