Long-wave flexural vibrations and deformation of a small size beam considering curface effects

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.