Cargando…

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

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 mathem...

Descripción completa

Detalles Bibliográficos
Autores principales: Zheng, Xinran, Huang, Mingqi, An, Dongqi, Zhou, Chao, Li, Rui
Formato: Online Artículo Texto
Lenguaje:English
Publicado: Nature Publishing Group UK 2021
Materias:
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7859414/
https://www.ncbi.nlm.nih.gov/pubmed/33536491
http://dx.doi.org/10.1038/s41598-021-82326-w
Descripción
Sumario: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.