New analytic bending, buckling, and free vibration solutions of rectangular nanoplates by the symplectic superposition method

Abstract New analytic bending, buckling, and free vibration solutions of rectangular nanoplates with combinations of clamped and simply supported edges are obtained by an up-to-date symplectic superposition method. The problems are reformulated in the Hamiltonian system and symplectic space, where t...

Descripción completa

Guardado en:

Detalles Bibliográficos
Autores principales:	Xinran Zheng, Mingqi Huang, Dongqi An, Chao Zhou, Rui Li
Formato:	article
Lenguaje:	EN
Publicado:	Nature Portfolio 2021
Materias:	Medicine R Science Q
Acceso en línea:	https://doaj.org/article/d3e4a6ced50747acaa8f239cdf1c1fe2
Etiquetas:	Agregar Etiqueta Sin Etiquetas, Sea el primero en etiquetar este registro!

id	oai:doaj.org-article:d3e4a6ced50747acaa8f239cdf1c1fe2
record_format	dspace
spelling	oai:doaj.org-article:d3e4a6ced50747acaa8f239cdf1c1fe22021-12-02T14:06:25ZNew analytic bending, buckling, and free vibration solutions of rectangular nanoplates by the symplectic superposition method10.1038/s41598-021-82326-w2045-2322https://doaj.org/article/d3e4a6ced50747acaa8f239cdf1c1fe22021-02-01T00:00:00Zhttps://doi.org/10.1038/s41598-021-82326-whttps://doaj.org/toc/2045-2322Abstract New analytic bending, buckling, and free vibration solutions of rectangular nanoplates with combinations of clamped and simply supported edges are obtained by an up-to-date symplectic superposition method. The problems are reformulated in the Hamiltonian system and symplectic space, where the mathematical solution framework involves the construction of symplectic eigenvalue problems and symplectic eigen expansion. The analytic symplectic solutions are derived for several elaborated fundamental subproblems, the superposition of which yields the final analytic solutions. Besides Lévy-type solutions, non-Lévy-type solutions are also obtained, which cannot be achieved by conventional analytic methods. Comprehensive numerical results can provide benchmarks for other solution methods.Xinran ZhengMingqi HuangDongqi AnChao ZhouRui LiNature PortfolioarticleMedicineRScienceQENScientific Reports, Vol 11, Iss 1, Pp 1-16 (2021)
institution	DOAJ
collection	DOAJ
language	EN
topic	Medicine R Science Q
spellingShingle	Medicine R Science Q Xinran Zheng Mingqi Huang Dongqi An Chao Zhou Rui Li New analytic bending, buckling, and free vibration solutions of rectangular nanoplates by the symplectic superposition method
description	Abstract New analytic bending, buckling, and free vibration solutions of rectangular nanoplates with combinations of clamped and simply supported edges are obtained by an up-to-date symplectic superposition method. The problems are reformulated in the Hamiltonian system and symplectic space, where the mathematical solution framework involves the construction of symplectic eigenvalue problems and symplectic eigen expansion. The analytic symplectic solutions are derived for several elaborated fundamental subproblems, the superposition of which yields the final analytic solutions. Besides Lévy-type solutions, non-Lévy-type solutions are also obtained, which cannot be achieved by conventional analytic methods. Comprehensive numerical results can provide benchmarks for other solution methods.
format	article
author	Xinran Zheng Mingqi Huang Dongqi An Chao Zhou Rui Li
author_facet	Xinran Zheng Mingqi Huang Dongqi An Chao Zhou Rui Li
author_sort	Xinran Zheng
title	New analytic bending, buckling, and free vibration solutions of rectangular nanoplates by the symplectic superposition method
title_short	New analytic bending, buckling, and free vibration solutions of rectangular nanoplates by the symplectic superposition method
title_full	New analytic bending, buckling, and free vibration solutions of rectangular nanoplates by the symplectic superposition method
title_fullStr	New analytic bending, buckling, and free vibration solutions of rectangular nanoplates by the symplectic superposition method
title_full_unstemmed	New analytic bending, buckling, and free vibration solutions of rectangular nanoplates by the symplectic superposition method
title_sort	new analytic bending, buckling, and free vibration solutions of rectangular nanoplates by the symplectic superposition method
publisher	Nature Portfolio
publishDate	2021
url	https://doaj.org/article/d3e4a6ced50747acaa8f239cdf1c1fe2
work_keys_str_mv	AT xinranzheng newanalyticbendingbucklingandfreevibrationsolutionsofrectangularnanoplatesbythesymplecticsuperpositionmethod AT mingqihuang newanalyticbendingbucklingandfreevibrationsolutionsofrectangularnanoplatesbythesymplecticsuperpositionmethod AT dongqian newanalyticbendingbucklingandfreevibrationsolutionsofrectangularnanoplatesbythesymplecticsuperpositionmethod AT chaozhou newanalyticbendingbucklingandfreevibrationsolutionsofrectangularnanoplatesbythesymplecticsuperpositionmethod AT ruili newanalyticbendingbucklingandfreevibrationsolutionsofrectangularnanoplatesbythesymplecticsuperpositionmethod
_version_	1718391991885103104

New analytic bending, buckling, and free vibration solutions of rectangular nanoplates by the symplectic superposition method

Ejemplares similares