Long-Wave Flexural Vibrations and Deformation of a Small Size Beam Considering Curface Effects
G. I. Mikhasev
Harbin Institute of Technology, Harbin, China
Keywords: micro/nano-beams, surface elasticity theory, asymptotic integration, shear, equation of motion, natural vibrations
Abstract
A small-sized elastic isotropic strip-beam loaded with variable body and surface forces is considered. On the front surfaces, surface shear stress and inertia are taken into account within the framework of the Gurtin-Murdoch surface elasticity theory. Asymptotically correct equations describing the long-wavelength bending deformation of micro/nano-beams taking into account shears and surface effects are derived by asymptotic integration of the two-dimensional elasticity equations over the strip thickness. The influence of surface stress and inertia on the lower spectrum of natural vibrations of metal micro/nano-beams is studied. It has been shown that surface inertia has the same effect on the spectrum of natural frequencies of bending vibrations as surface stresses.
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