Vibration analysis of nano-beams based on differential transform method

According to application of nano-beams as nano-sensors, actuators, nano-generators, transistors, diodes and resonators in nano-electromechanical systems and in biotechnology it is important to investigate the vibrational behavior of nano-beams. In this study, the differential transformation method (DTM) is employed for vibration analysis of size-dependent nano-beams considering the coupled surface and nonlocality effects for various boundary conditions. The Eringen¿s nonlocal elasticity theory takes into account the effect of small size while the Gurtin-Murdoch model is used to incorporate the surface effects. The derived governing differential equation solved by DTM which demonstrated to have high precision and computational efficiency in the vibration analysis of nano-beams.