Nonlocal Elasticity Theory for Transient Analysis of Higher-Order Shear Deformable Nanoscale Plates

• Published in: Journal of nanomaterials 2014-01, Vol.2014 (2014), p.1-8
• Main Authors: Jung, Woo Young, Han, Sung-Cheon
• Format: Article
• Language: English
• Subjects: Boundary conditions; Dynamic response; Mathematical models; Mechanics; Nanomaterials; Nanostructure; Nonlocal elasticity; Plates; Shear deformation; Shear strain; Small scale; Studies; Theory; Transient analysis; Vibration analysis
• ISSN: 1687-4110; 1687-4129
• DOI: 10.1155/2014/208393

The small scale effect on the transient analysis of nanoscale plates is studied. The elastic theory of the nano-scale plate is reformulated using Eringen’s nonlocal differential constitutive relations and higher-order shear deformation theory (HSDT). The equations of motion of the nonlocal theories are derived for the nano-scale plates. The Eringen’s nonlocal elasticity of Eringen has ability to capture the small scale effects and the higher-order shear deformation theory has ability to capture the quadratic variation of shear strain and consequently shear stress through the plate thickness. The solutions of transient dynamic analysis of nano-scale plate are presented using these theories to illustrate the effect of nonlocal theory on dynamic response of the nano-scale plates. On the basis of those numerical results, the relations between nonlocal and local theory are investigated and discussed, as are the nonlocal parameter, aspect ratio, side-to-thickness ratio, nano-scale plate size, and time step effects on the dynamic response. In order to validate the present solutions, the reference solutions are employed and examined. The results of nano-scale plates using the nonlocal theory can be used as a benchmark test for the transient analysis.