Polysilicon nano-beam model based on modified couple stress and Eringen’s nonlocal elasticity theories

• An analytical solution for the static pull-in voltage is derived.
• Polysilicon nano-beam is modeled using non-classical continuum theories.
• Natural frequencies of several micro-beams are compared to the experimental ones.
• Modified couple stress theory is in better agreement with experimental results.

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.

In this paper, polysilicon nano-beam is modeled based on modified couple stress and Eringen’s nonlocal elasticity theories.Figure optionsDownload as PowerPoint slide