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

The classical Euler–Bernoulli beam model and Kirchhoff plate are very useful on the macroscopic scale. In context of Eringen’s nonlocal elasticity theory, this article aims to develop criteria applicability nanoscale models based Timoshenko Mindlin via wave propagation theory. corresponding governing differential equations for derived by Hamilton’s principle, dispersion then obtained. By applying Taylor expansion solutions equations, new developed, simultaneously taking into account effects parameters material properties. When parameter is set zero, present may be readily degenerated their counterparts. According criteria, systematically evaluates existing studies in literature. Various works literature did not consider effect parameter, hence, failed satisfy application conditions nanoscale. work scientific significance various nanostructures.