Surface effect on the resonant frequency of Timoshenko nanobeams

The dynamic behavior of a Timoshenko nanobeam would be significantly different from a macro-one due to the large ratio of surface area to volume of nanomaterials. Furthermore, the shear deformation effect would be obvious for a Timoshenko nanobeam in contrast to an Eulerian one. In this paper, a recently developed elastic theory is adopted in order to predict the resonant frequency of a Timoshenko nanobeam, in which not only the surface effect but also the shear deformation effect and the rotary inertia one are considered. In contrast to the existing surface effect theories, surface effect of nanomaterials is characterized by the surface energy density in the adopted theory. The resonant frequency of both a fixed-fixed nanobeam and a cantilevered one is analyzed. It is found that the dynamic behavior of nanobeams deviates significantly from the one predicted by both the classical Timoshenko beam theory and the Euler–Bernoulli one due to the surface effect. Furthermore, the shear deformation effect and the rotary inertia effect cannot be neglected in nanobeams with a relative small aspect ratio, which cannot be precisely characterized by the Euler–Bernoulli beam theory. In addition, the influencing mechanism of surface effect on the dynamic behavior of nanobeams would depend on the boundary conditions. The resonant frequency of a fixed–fixed Timoshenko nanobeam would be improved, while that of a cantilevered one would be weakened by the surface effect in contrast to the corresponding classical solutions. The results in this paper should be useful for precise design of nano-devices and helpful for reasonable assessment of test results of nano-instruments.