In this paper, a comprehensive model is presented to investigate the influence of surface elasticity and residual surface tension on the natural frequency of flexural vibrations of microbeams in the presence of rotary inertia and shear deformation effects. An explicit solution is derived for the natural oscillations of microscaled Timoshenko beams considering surface effects. The analytical results are illustrated with numerical examples in which two types of microbeams are configured based on Euler–Bernoulli and Timoshenko beam theory considering surface elasticity and residual surface tension. The natural frequencies of vibration are calculated for selected beam length on the order of nanometer to microns and the results are compared with those corresponding to the classical beam models, emphasizing the differences occurring when the surface effects are significant. It is found that the nondimensional natural frequency of the vibration of micro and nanoscaled beams is size dependent and for limiting case in which the beam length increases, the results tends to the results obtained by classical beam models. This study might be helpful for the design of high-precision measurement devices such as chemical and biological sensors.
a b s t r a c tThe effect of the interface stresses is studied upon the size-dependent elastic deformation of an elastic half-plane having a cylindrical inclusion with distinct elastic properties. The elastic half-plane is subjected to either a uniaxial loading at infinity or a uniform non-shear eigenstrain in the inclusion. The straight edge of the half-plane is either traction-free, or rigid-slip, or motionless, which represents three practical situations of mechanical structures. Using two-dimensional Papkovich-Neuber potentials and the theory of surface/interface elasticity, the elastic field in the elastic half-plane is obtained. Comparable with classical result, the new formulation renders the significant effect of the interface stresses on the stress distribution in the half-plane when the radius of the inclusion is reduced to the nanometer scale. Numerical results show that the intensity of the influence depends on the surface/interface moduli, the stiffness ratio of the inclusion to the surrounding material, the boundary condition on the edge of the half-plane and the proximity of the inclusion to the edge.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.