Article ID Journal Published Year Pages File Type
1545628 Physica E: Low-dimensional Systems and Nanostructures 2010 6 Pages PDF
Abstract

A modified continuum model of the nanoscale beams is presented by incorporating surface elasticity in this paper. The classical beam theory is adopted to model the bulk, while the bulk stresses along the surfaces of the bulk substrate are required to satisfy the surface balance equations of the continuum surface elasticity. On the basis of this modified beam theory the governing equation of the nanobeam is derived where the effect of the geometry nonlinearity is also considered. The Galerkin method is used to give a reduced-order model of the problem. Beams made from two materials: aluminum and silicon are chosen as examples. The numerical results show that the mechanical buckling and free vibration phenomena of nanobeams are size-dependence. The effects of the surface energies on the critical axial force of buckling, post-buckling and linear free vibration frequency are discussed. Finally, the amplitude frequency response is given numerically through the incremental harmonic balanced method.

Related Topics
Physical Sciences and Engineering Materials Science Electronic, Optical and Magnetic Materials
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