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 are modeled as beams and governing vibration equations derived considering compatibility conditions in sections. Then, an analytical solution is developed to simulate natural frequencies mode shapes nanobeam with various properties. Also, a backward procedure proposed verify obtained results calculate effective modulus. The indicate that effects appropriate steps selection have noticeable impact on non-uniform nanobeams. modeling became more important for longer slender ones. Moreover, despite uniform nanobeams, also extremely dependent effects.