Keywords:

nanostructures. This theory, developed by Eringen, has shown to be practical for the vibration and buck-systems (NOMS), nanocomposites, nanosensors, nanoactuators and biomedical systems [26–30]. Many of the above mention types of single or multi-nanoplate systems, bounded with certain type of medium, can be theoreti-cally modeled using the same phenomenological assumptions as in case of classical plate systems [31,32]. However, experimental investigations [33,34] and atomistic simulations [35] have shown lti-layered graph-vdW) interaction models. A ic forces in sis of nano-scale structures is to use the nonlocal elasticity of Eringen [40]. This theory is used in numerous studies o strucures and it is often used for reliable and fast analysis. The multi-nanoplate system considered in this paper is different from multi-layer or double-layer systems presented in [37–39,41]. This difference is reflected in the fact that mentioned multi-layer and double-layer systems are bonded by a constant vdW force while the multi-nanoplate systems are bonded by an elastic medium with certain stiffness. The system studied here is particu-larly relevant to the future generation graphene based composit