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Nanoscale materials and structures have recently received considerable interest as sensors and devices.Research on vibration of such small apparatus and their components, such as nano-electromechanical system (NEMS).is important in nanotechnology.Vibration of many structures in nanometer scales can be modelled as the transverse vibration of nanobeams, of which some are the fully clamped beams according to their boundary constraints.In fact.fully clamped condition is one of the most important boundary types and it is easily to be seen in NEMS.However.in recent years, the literature regarding the vibration behavior of macro beams is plenty, but the vibration analysis of nanoscale beams has not been investigated systematically due to the lack of a new vibration model which is adapted to small size effects.