UBC Theses and Dissertations
Surface elasticity models for static and dynamic response of nanoscale beams Chang, Liu
Nanoscale beam-like structures have attracted much attention due to their superior mechanical properties for applications in nanomechanical and nanoelectromechanical systems (NEMS). Nanoscale structures are characterized by a high surface to volume ratio. The elastic response of surface layers of atoms is different from that of the bulk atoms due to reduced connectivity. Thus, surface energy has a significant effect on the response of nanoscale structures, and is associated with their size-dependent behavior. The classical continuum mechanics fails to capture the surface energy effects and hence is not directly applicable at nanoscale. To overcome this limitation, modified continuum models incorporating surface energy effects need to be developed in order to evaluate the size-dependent mechanical response of nanoscale structures. This thesis presents a modified continuum model and finite element formulation to study the static and dynamic response of nanoscale beams. The objective is to provide NEMS designers with an efficient set of tools that can predict static deflections, natural frequencies of vibrations, and uniaxial buckling loads of nanoscale beams with different geometries, applied forces, and boundary conditions. A general beam model based on Gurtin-Murdoch continuum surface elasticity theory is developed for the analysis of thin and thick beams of arbitrary cross-section. Closed-form analytical solutions for static bending of thin and thick beams under different loadings and boundary conditions are obtained. Their free vibration characteristics are also investigated. Analytical expressions for critical buckling loads of thin beam are presented. An intrinsic length scale depending on both surface and bulk elastic properties is defined to characterize surface energy effects in beam bending problems. The finite element simulation results of static bending, free vibration and axial buckling of nanoscale beams are compared with the analytical solutions for validation. Selected numerical results are presented for aluminum and silicon beams to demonstrate their salient response features. A technique is proposed to estimate surface elastic properties from measured natural frequencies of GaAs cantilever specimen. The surface elasticity continuum mechanics and finite element models developed in this work provide designers efficient tools to predict mechanical response of beam structures in nano devices.
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