Asymptotically consistent size-dependent plate models based on the couple-stress theory with micro-inertia

Several beam and plate models have been recently developed in the literature to accommodate for size-dependence. These are usually obtained starting from a generalized continuum theory (such as couple-stress, strain-gradient or non-local their modifications) then deducing governing equations through Hamilton’s principle ingenuous kinematical assumptions. This approach, originated by Kirchhoff, fails reproduce dispersion features of equivalent 3D theory. Besides, it produces variety models, dependence different assumptions, such Kirchhoff’s Mindlin’s. In contrast, this paper we adopt asymptotic reduction: moving couple-stress linear elasticity with micro-inertia, deduce new elongation flexural deformation microstructured plates. The resulting consistent, sense that they corresponding body. Also, unique, may only differ order approximation. We find microstructure especially affects inertia terms, which can be hardly captured a-priori For static deformations, our results match those already assuming plane cross-sections within modified fact, show reduced strain gradient theories all lead results. Higher also given, describe near first-cut-off behaviour account thickness deformations spirit Timoshenko.