AI Article Synopsis
- The study presents new analytical solutions for bending, buckling, and vibrations of rectangular nanoplates with different edge conditions using a modern symplectic superposition method.
- The research reformulates the issues in a Hamiltonian framework, utilizing symplectic space to create symplectic eigenvalue problems and solutions that help solve complex subproblems.
- This method produces both Lévy-type and non-Lévy-type solutions, expanding on traditional analytical methods, and offers numerical results that serve as benchmarks for further research.
Article 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.
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| http://www.ncbi.nlm.nih.gov/pmc/articles/PMC7859414 | PMC |
| http://dx.doi.org/10.1038/s41598-021-82326-w | DOI Listing |
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