Transversely Vibration of Nanobeams using Four Beam Theories

In this paper, transversely vibration analysis of nanobeams based on four Beam theories is investigated. There are several kinds of beam theories, including the Euler-Bernoulli, Rayleigh, Shear and Timoshenko beam theories, are reformulated by the nonlocal differential constitutive relations of Eringen. Analytical solutions of nanobeams vibration are presented using the nonlocal theories to bring out the small scale, rotary inertia and shear deformation influence on natural frequencies behavior of nanobeams. Another illustration of the small scale, rotary inertia and shear deformation effects are also shown by obtained results of single-walled carbon nanotube (SWCNT).