Green Functions for Axisymmetric Bending and Vibration of Thick Cylindrical Shells

Abstract

It is shown herein that the axisymmetric bending and vibration problems of thick (Mindlin) cylindrical shells are analogous to the corresponding bending and vibration problems of Timoshenko beams resting on Winkler foundation. The Green functions for solving these two analogous problems are derived. Based on these Green functions, exact bending and vibration results may be obtained. The validity of the solutions has been verified via comparison studies with previous researchers' numerical results. Sample exact bending and vibration results are also presented for cylindrical shells in view to provide useful benchmark checks for researchers and engineers working on cylindrical shells and Timoshenko beams on elastic foundation.

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