NONLOCAL SECOND-ORDER SHEAR DEFORMATION PLATE THEORY FOR FREE VIBRATION OF NANOPLATES
Keywords:
Nanoplates, free vibration, second-order shear deformation, nonlocal elasticity, simplesupport, analytical solutionAbstract
In this paper, the second-order shear deformation plate theory is developed for the study of the natural frequencies of rectangular nanoplates based on the nonlocal elasticity theory of Eringen. The governing equation of nanoplates is derived by using Hamilton’s principle. The analytical solution for the natural frequencies and corresponding mode shapes of simply supported nanoplates is established. The effects of nonlocal parameters, the plate aspect ratios, and the plate thicknesses on the free vibration response are investigated. The obtained results show good agreement with other available solutions. The formulation and these analytical results of the proposed method could serve as a benchmark in the evaluation of future research.
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