Long-Wave Flexural Vibrations and Deformation of a Small-Size Beam Considering Surface Effects

Abstract

A small-size elastic isotropic beam-strip loaded by variable body and surface forces is considered. On the front surfaces, surface shear stresses 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- and 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 stresses and inertia on the lower spectrum of natural vibrations of metal micro- and nano-beams is studied. It is shown that surface inertia has the same effect on the frequency spectrum of natural flexural vibrations as surface stresses.