A New Hamiltonian Semi-Analytical Approach to Vibration Analysis of Piezoelectric Multi-Layered Plates
A new Hamiltonian semi-analytical method is established to investigate the free vibration characteristics of piezoelectric multilayered plates. By performing a Legendre Transform, the classical Lagrangian functional is recast into a Hamiltonian one, so that the resulting variational formulation can...
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2024
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| Online Access: | https://hdl.handle.net/11073/25817 |
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| _version_ | 1864513444564172800 |
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| author | Andrianarison, O. |
| author2 | Benjeddou, Ayech |
| author2_role | author |
| author_facet | Andrianarison, O. Benjeddou, Ayech |
| author_role | author |
| dc.creator.none.fl_str_mv | Andrianarison, O. Benjeddou, Ayech |
| dc.date.none.fl_str_mv | 2024-11 2025-01-29T07:53:25Z 2025-01-29T07:53:25Z |
| dc.format.none.fl_str_mv | application/pdf |
| dc.identifier.none.fl_str_mv | Andrianarisona, O., & Benjeddou, A. (2025, January 23). A New Hamiltonian Semi-Analytical Approach to Vibration Analysis of Piezoelectric Multi-Layered Plates. https://doi.org/10.5281/zenodo.14725507 https://hdl.handle.net/11073/25817 10.5281/zenodo.14725507 |
| dc.language.none.fl_str_mv | en |
| dc.publisher.none.fl_str_mv | American University of Sharjah |
| dc.relation.none.fl_str_mv | 8th International Conference on Smart Materials & Nanotechnology in Engineering (SMN2024) https://doi.org/10.5281/zenodo.14725507 |
| dc.rights.none.fl_str_mv | Attribution 4.0 International http://creativecommons.org/licenses/by/4.0/ |
| dc.subject.none.fl_str_mv | Hamiltonian Semi-analytic Spectral finite element Vibration Piezoelectric Multilayer Plate |
| dc.title.none.fl_str_mv | A New Hamiltonian Semi-Analytical Approach to Vibration Analysis of Piezoelectric Multi-Layered Plates |
| dc.type.none.fl_str_mv | info:eu-repo/semantics/publishedVersion info:eu-repo/semantics/article |
| description | A new Hamiltonian semi-analytical method is established to investigate the free vibration characteristics of piezoelectric multilayered plates. By performing a Legendre Transform, the classical Lagrangian functional is recast into a Hamiltonian one, so that the resulting variational formulation can be expressed in terms of the displacements and electric potential and their transverse stresses and electric displacement dual variables. Within the framework of this Hamiltonian formalism, the in-plane of the piezoelectric multilayered plate is discretized into two-dimensional p-type high-order spectral finite elements while the resulting first-order one dimensional differential system is solved analytically by enforcing the interface continuity constraints. The whole piezoelectric multilayered plate’s dynamic stiffness is then built, from which its circular frequencies are computed with the help of the Wittrick-Williams algorithm. A detailed discussion is provided on the implementation aspects, followed by some numerical examples to assess the robustness, accuracy and effectiveness of the proposed method. The obtained results are verified by comparison with published ones based on conventional approaches. |
| format | article |
| id | aus_d9625567e3ab1d629d397bb535d246c9 |
| identifier_str_mv | Andrianarisona, O., & Benjeddou, A. (2025, January 23). A New Hamiltonian Semi-Analytical Approach to Vibration Analysis of Piezoelectric Multi-Layered Plates. https://doi.org/10.5281/zenodo.14725507 10.5281/zenodo.14725507 |
| language_invalid_str_mv | en |
| network_acronym_str | aus |
| network_name_str | aus |
| oai_identifier_str | oai:repository.aus.edu:11073/25817 |
| publishDate | 2024 |
| publisher.none.fl_str_mv | American University of Sharjah |
| repository.mail.fl_str_mv | |
| repository.name.fl_str_mv | |
| repository_id_str | |
| rights_invalid_str_mv | Attribution 4.0 International http://creativecommons.org/licenses/by/4.0/ |
| spelling | A New Hamiltonian Semi-Analytical Approach to Vibration Analysis of Piezoelectric Multi-Layered PlatesAndrianarison, O.Benjeddou, AyechHamiltonianSemi-analyticSpectral finite elementVibrationPiezoelectricMultilayerPlateA new Hamiltonian semi-analytical method is established to investigate the free vibration characteristics of piezoelectric multilayered plates. By performing a Legendre Transform, the classical Lagrangian functional is recast into a Hamiltonian one, so that the resulting variational formulation can be expressed in terms of the displacements and electric potential and their transverse stresses and electric displacement dual variables. Within the framework of this Hamiltonian formalism, the in-plane of the piezoelectric multilayered plate is discretized into two-dimensional p-type high-order spectral finite elements while the resulting first-order one dimensional differential system is solved analytically by enforcing the interface continuity constraints. The whole piezoelectric multilayered plate’s dynamic stiffness is then built, from which its circular frequencies are computed with the help of the Wittrick-Williams algorithm. A detailed discussion is provided on the implementation aspects, followed by some numerical examples to assess the robustness, accuracy and effectiveness of the proposed method. The obtained results are verified by comparison with published ones based on conventional approaches.American University of Sharjah2025-01-29T07:53:25Z2025-01-29T07:53:25Z2024-11info:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articleapplication/pdfAndrianarisona, O., & Benjeddou, A. (2025, January 23). A New Hamiltonian Semi-Analytical Approach to Vibration Analysis of Piezoelectric Multi-Layered Plates. https://doi.org/10.5281/zenodo.14725507https://hdl.handle.net/11073/2581710.5281/zenodo.14725507en8th International Conference on Smart Materials & Nanotechnology in Engineering (SMN2024)https://doi.org/10.5281/zenodo.14725507Attribution 4.0 Internationalhttp://creativecommons.org/licenses/by/4.0/oai:repository.aus.edu:11073/258172025-01-30T10:36:30Z |
| spellingShingle | A New Hamiltonian Semi-Analytical Approach to Vibration Analysis of Piezoelectric Multi-Layered Plates Andrianarison, O. Hamiltonian Semi-analytic Spectral finite element Vibration Piezoelectric Multilayer Plate |
| status_str | publishedVersion |
| title | A New Hamiltonian Semi-Analytical Approach to Vibration Analysis of Piezoelectric Multi-Layered Plates |
| title_full | A New Hamiltonian Semi-Analytical Approach to Vibration Analysis of Piezoelectric Multi-Layered Plates |
| title_fullStr | A New Hamiltonian Semi-Analytical Approach to Vibration Analysis of Piezoelectric Multi-Layered Plates |
| title_full_unstemmed | A New Hamiltonian Semi-Analytical Approach to Vibration Analysis of Piezoelectric Multi-Layered Plates |
| title_short | A New Hamiltonian Semi-Analytical Approach to Vibration Analysis of Piezoelectric Multi-Layered Plates |
| title_sort | A New Hamiltonian Semi-Analytical Approach to Vibration Analysis of Piezoelectric Multi-Layered Plates |
| topic | Hamiltonian Semi-analytic Spectral finite element Vibration Piezoelectric Multilayer Plate |
| url | https://hdl.handle.net/11073/25817 |