New criteria for nanoscale slender beams and thin plates: Low frequency domain of flexural wave

Abstract

The appropriateness of the Euler-Bernoulli beam model and the Kirchhoff plate model, which were adopted in the existing studies to characterize nanoplates and nanobeams, would be checked by the present criteria. To this end, numerous studies in literature are chosen, where the Euler-Bernoulli beam model or the Kirchhoff plate model was adopted. All the data in the tables originate directly from the references, and the frequencies  satisfy Eqs. ( 7) or (B.21) in the main text. The shear correction factor  tends to infinity since shear deformations were not considered in these two classical models.