A Comparison of Three Theories for Vibration Analysis for Shell Models - Maria Anna De Rosa; Isaac Elishakoff; Maria Lippiello (CivilEng)
Shells are significant structural components that are extensively utilized in numerous engineering fields, including architectural and infrastructural projects. These components are employed in the construction of domes, water tanks, stadiums and auditoriums, hangars, and cooling towers. Significant research efforts have been dedicated to the analysis of vibrations and dynamic behaviors of shells, due to their distinctive capacity to efficiently bear loads through their geometry rather than mass. Additionally, a vast array of shell theories and computational methods have been proposed and developed by researchers. This paper represents a continuation of research initiated begun in a 2009 paper by Elishakoff, wherein the suggestion was made to disregard an energetic term in the dynamic analysis of Timoshenko–Ehrenfest beams, wherein the suggestion was made to disregard an energetic term in the dynamic analysis of Timoshenko–Ehrenfest beams. The resulting reduced theory was found to be both more straightforward and more reliable than the complete, classical approach. While the original idea was heuristically justified, a more sound variationally consistent theory was proposed in the papers of De Rosa et al. concerning the dynamic analysis of the Timoshenko-Ehrenfest beams and later extended to the case of the Uflyand-Mindlin plates. In accordance with the proposal put forth in those works, we initially delineate the classical shell theory and subsequently propose two alternative hypotheses that give rise to two distinct aspects of the energy terms. By employing the variational approach, we derive two novel boundary problems, which are direct generalizations of those previously considered. Both theories can be readily specialized for beams and plates, and the theory can also be specialized for the case of cylindrical shells.