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Polysilicon nano-beam model based on modified couple stress and Eringen's nonlocal elasticity theories
Miandoab, E. M ; Sharif University of Technology
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- Type of Document: Article
- DOI: 10.1016/j.physe.2014.05.025
- Abstract:
- In recent years, extensive experiments have shown that classical continuum theory cannot predict the behavior of mechanical microstructures with small size. To accurately design and analyze micro- and nano-electro-mechanical systems, size-dependent continuum theories should be used. These theories model micro- and nano-electro-mechanical systems with higher accuracy because they include size-dependent parameters. In this paper, polysilicon nano-beam is modeled using modified couple stress and Eringen's nonlocal elasticity theories. First, partial differential equations governing the vibration of nano-beams are converted to a one D.O.F. differential equations using Galerkin method, resulting in the lumped model of the system. Then, an analytical solution for the static pull-in voltage is derived from the lumped model of the system and Taylor expansion of the electrostatic force with fringing field effect. Both clamped-free and clamped-clamped beams are considered in the analysis where the mid-plane stretching and axial force are taken into account in clamped-clamped case. The method and model are validated by comparing the results with previously reported ones in the literature. Size-dependent parameters of polysilicon are chosen in order to minimize the difference between calculated and experimental values for static pull-in voltages. Natural frequencies of several micro-beams are calculated using derived non-classical models and results are compared to the experimental ones. The results demonstrate that modified couple stress theory coincides experimental results better than Eringen's nonlocal elasticity and classical theories
- Keywords:
- Eringen's nonlocal elasticity theory ; Modified couple stress ; Polysilicon ; Size effect ; Continuum mechanics ; Differential equations ; Elasticity ; Galerkin methods ; Machine design ; Mechanical engineering ; Classical continuum theory ; Fringing field effects ; Modified couple stress theories ; Nano electromechanical systems ; Non-local elasticities ; Non-local elasticity theories ; Size effects
- Source: Physica E: Low-Dimensional Systems and Nanostructures ; Vol. 63, issue , 2014 , p. 223-228
- URL: http://www.sciencedirect.com/science/article/pii/S1386947714002094