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Symplectic superposition solutions for free in-plane vibration of orthotropic rectangular plates with general boundary conditions

This work reports new analytic free in-plane vibration solutions for orthotropic non-Lévy-type rectangular plates, i.e., those without two opposite edges simply supported, by the symplectic superposition method (SSM), which has never been applied to in-plane elasticity problems in any existing works...

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Autores principales: Hu, Zhaoyang, Du, Jingyu, Liu, Mingfeng, Li, Yihao, Wang, Zixuan, Zheng, Xinran, Quoc Bui, Tinh, Li, Rui
Formato: Online Artículo Texto
Lenguaje:English
Publicado: Nature Publishing Group UK 2023
Materias:
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC9929225/
https://www.ncbi.nlm.nih.gov/pubmed/36788236
http://dx.doi.org/10.1038/s41598-023-29044-7
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author Hu, Zhaoyang
Du, Jingyu
Liu, Mingfeng
Li, Yihao
Wang, Zixuan
Zheng, Xinran
Quoc Bui, Tinh
Li, Rui
author_facet Hu, Zhaoyang
Du, Jingyu
Liu, Mingfeng
Li, Yihao
Wang, Zixuan
Zheng, Xinran
Quoc Bui, Tinh
Li, Rui
author_sort Hu, Zhaoyang
collection PubMed
description This work reports new analytic free in-plane vibration solutions for orthotropic non-Lévy-type rectangular plates, i.e., those without two opposite edges simply supported, by the symplectic superposition method (SSM), which has never been applied to in-plane elasticity problems in any existing works. Such analytic solutions are not accessible through conventional analytic methods as seeking analytic solutions that meet both the governing partial differential equations and various non-Lévy-type boundary conditions is an acknowledged challenge in mechanical analysis of plates. The clamped and free plates are considered as two most representative cases of non-Lévy-type plates. The SSM is implemented in the Hamiltonian system-based symplectic space, where the separation of variables and the symplectic eigen expansion prove to be well-grounded. These two mathematical treatments are adopted to first gain the analytic solutions of two elementary problems. The final analytic free in-plane vibration solutions are obtained by superposition of the two elementary problems. Comprehensive new natural frequencies and vibration modes are studied and validated by reference solutions from the finite element method or other approaches. The rigorous solution procedure, fast convergence, and highly accurate results render the present framework capable of serving as benchmarks for future comparison and applicable to analytic investigation of more plate problems.
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spelling pubmed-99292252023-02-16 Symplectic superposition solutions for free in-plane vibration of orthotropic rectangular plates with general boundary conditions Hu, Zhaoyang Du, Jingyu Liu, Mingfeng Li, Yihao Wang, Zixuan Zheng, Xinran Quoc Bui, Tinh Li, Rui Sci Rep Article This work reports new analytic free in-plane vibration solutions for orthotropic non-Lévy-type rectangular plates, i.e., those without two opposite edges simply supported, by the symplectic superposition method (SSM), which has never been applied to in-plane elasticity problems in any existing works. Such analytic solutions are not accessible through conventional analytic methods as seeking analytic solutions that meet both the governing partial differential equations and various non-Lévy-type boundary conditions is an acknowledged challenge in mechanical analysis of plates. The clamped and free plates are considered as two most representative cases of non-Lévy-type plates. The SSM is implemented in the Hamiltonian system-based symplectic space, where the separation of variables and the symplectic eigen expansion prove to be well-grounded. These two mathematical treatments are adopted to first gain the analytic solutions of two elementary problems. The final analytic free in-plane vibration solutions are obtained by superposition of the two elementary problems. Comprehensive new natural frequencies and vibration modes are studied and validated by reference solutions from the finite element method or other approaches. The rigorous solution procedure, fast convergence, and highly accurate results render the present framework capable of serving as benchmarks for future comparison and applicable to analytic investigation of more plate problems. Nature Publishing Group UK 2023-02-14 /pmc/articles/PMC9929225/ /pubmed/36788236 http://dx.doi.org/10.1038/s41598-023-29044-7 Text en © The Author(s) 2023 https://creativecommons.org/licenses/by/4.0/Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article's Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article's Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/ (https://creativecommons.org/licenses/by/4.0/) .
spellingShingle Article
Hu, Zhaoyang
Du, Jingyu
Liu, Mingfeng
Li, Yihao
Wang, Zixuan
Zheng, Xinran
Quoc Bui, Tinh
Li, Rui
Symplectic superposition solutions for free in-plane vibration of orthotropic rectangular plates with general boundary conditions
title Symplectic superposition solutions for free in-plane vibration of orthotropic rectangular plates with general boundary conditions
title_full Symplectic superposition solutions for free in-plane vibration of orthotropic rectangular plates with general boundary conditions
title_fullStr Symplectic superposition solutions for free in-plane vibration of orthotropic rectangular plates with general boundary conditions
title_full_unstemmed Symplectic superposition solutions for free in-plane vibration of orthotropic rectangular plates with general boundary conditions
title_short Symplectic superposition solutions for free in-plane vibration of orthotropic rectangular plates with general boundary conditions
title_sort symplectic superposition solutions for free in-plane vibration of orthotropic rectangular plates with general boundary conditions
topic Article
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC9929225/
https://www.ncbi.nlm.nih.gov/pubmed/36788236
http://dx.doi.org/10.1038/s41598-023-29044-7
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