1. New closed-form solutions for flexural vibration and eigen-buckling of nanoplates based on the nonlocal theory of elasticity.
- Author
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Ni, Hua, Tian, Yifeng, Xiang, Wei, and He, Lina
- Subjects
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MECHANICAL buckling , *RECTANGULAR plates (Engineering) , *SEPARATION of variables , *DIFFERENTIAL forms , *DIFFERENTIAL equations , *ELASTICITY , *EIGENVALUE equations - Abstract
This paper investigates the size-dependent vibration and buckling behavior of nanoplates described by the nonlocal Kirchhoff model analytically. The nonlocal and local constitutive relations, governing equations and boundary conditions are comprehensively discussed. A shifted governing equation in terms of local stress resultants with associated local boundary conditions is chosen in the current work. The direct separation of variables method is formulated based on the Hamiltonian dual form of the governing differential equation to address the eigenvalue problems of nonlocal rectangular plates with each edge either simply supported or clamped. The closed-form eigen-solutions are acquired for the first time for the cases where two adjacent clamped edges exist. The validity and accuracy of the present approach are verified by comparison with published analytical and numerical results. Parametric studies are performed to investigate the influences of nonlocal parameter and boundary conditions on the size-dependency of natural frequencies and critical buckling loads of nanoplates. [ABSTRACT FROM AUTHOR]
- Published
- 2023
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