Size-dependent Vibration Analysis of Stepped Nanobeams Based on Surface Elasticity Theory

This paper investigates size-dependent vibrations of stepped nanobeams taken into account surface elasticity theory. To do this, the nanobeams are modeled as stepped beams and size-dependent governing vibration equations are derived considering compatibility conditions in stepped sections. Then, an analytical solution is developed to simulate natural frequencies and mode shapes of the nanobeam with various surface properties. Also, a backward procedure is proposed to verify the obtained results and calculate size-dependent effective surface modulus. The results indicate that surface effects and appropriate steps selection have noticeable impact on natural frequencies of nonuniform nanobeams. Also, the stepped modeling of the nanobeam became more important for longer and slender ones. Moreover, despite uniform nanobeams, the mode shapes of the non-uniform nanobeams are also extremely dependent on the surface effects.