A Comparison of Three Theories for Vibration Analysis for Shell Models

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...

Full description

Saved in:
Bibliographic Details
Main Authors: Maria Anna De Rosa, Isaac Elishakoff, Maria Lippiello
Format: Article
Language:English
Published: MDPI AG 2025-03-01
Series:CivilEng
Subjects:
Online Access:https://www.mdpi.com/2673-4109/6/1/13
Tags: Add Tag
No Tags, Be the first to tag this record!
_version_ 1849343289037160448
author Maria Anna De Rosa
Isaac Elishakoff
Maria Lippiello
author_facet Maria Anna De Rosa
Isaac Elishakoff
Maria Lippiello
author_sort Maria Anna De Rosa
collection DOAJ
description 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.
format Article
id doaj-art-0e56cbd2fa6c4ba2854ec0a75929b25c
institution Kabale University
issn 2673-4109
language English
publishDate 2025-03-01
publisher MDPI AG
record_format Article
series CivilEng
spelling doaj-art-0e56cbd2fa6c4ba2854ec0a75929b25c2025-08-20T03:43:02ZengMDPI AGCivilEng2673-41092025-03-01611310.3390/civileng6010013A Comparison of Three Theories for Vibration Analysis for Shell ModelsMaria Anna De Rosa0Isaac Elishakoff1Maria Lippiello2School of Engineering, University of Basilicata, 85100 Potenza, ItalyDepartment of Ocean and Mechanical Engineering, Florida Atlantic University, Boca Raton, FL 33431-0991, USADepartment of Structures for Engineering and Architecture, University of Naples “Federico II”, Via Forno Vecchio, 36, 80134 Naples, ItalyShells 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.https://www.mdpi.com/2673-4109/6/1/13thick shellvibrationvariational formulation
spellingShingle Maria Anna De Rosa
Isaac Elishakoff
Maria Lippiello
A Comparison of Three Theories for Vibration Analysis for Shell Models
CivilEng
thick shell
vibration
variational formulation
title A Comparison of Three Theories for Vibration Analysis for Shell Models
title_full A Comparison of Three Theories for Vibration Analysis for Shell Models
title_fullStr A Comparison of Three Theories for Vibration Analysis for Shell Models
title_full_unstemmed A Comparison of Three Theories for Vibration Analysis for Shell Models
title_short A Comparison of Three Theories for Vibration Analysis for Shell Models
title_sort comparison of three theories for vibration analysis for shell models
topic thick shell
vibration
variational formulation
url https://www.mdpi.com/2673-4109/6/1/13
work_keys_str_mv AT mariaannaderosa acomparisonofthreetheoriesforvibrationanalysisforshellmodels
AT isaacelishakoff acomparisonofthreetheoriesforvibrationanalysisforshellmodels
AT marialippiello acomparisonofthreetheoriesforvibrationanalysisforshellmodels
AT mariaannaderosa comparisonofthreetheoriesforvibrationanalysisforshellmodels
AT isaacelishakoff comparisonofthreetheoriesforvibrationanalysisforshellmodels
AT marialippiello comparisonofthreetheoriesforvibrationanalysisforshellmodels