Nonlocal vibration of bonded double-nanoplate-systems

Nonlocal vibration of a double-nanoplate-system is considered. The two nanoplates are assumed to be bonded by an enclosing elastic medium. Situation of this type would arise in multiple graphene sheets dispersed in nanocomposites. Expressions for free bending-vibration of double-nanoplate-system are established utilising nonlocal elasticity. An analytical method is introduced for determining the natural frequencies of nonlocal double-nanoplate-system (NDNPS). Explicit closed-form expressions for natural frequencies are derived for the case when all four ends are simply-supported. Two single-layered graphene sheets coupled within bonding polymer matrix are considered. The study highlights that the small-scale effects considerably influence the transverse vibration of NDNPS. The small-scale effects in NDNPS are higher with the increasing values of nonlocal parameter for the case of synchronous modes of vibration than in the asynchronous modes. The increase of the stiffness of the coupling springs in NDNPS reduces the small-scale effects during the asynchronous modes of vibration. Further, the effect of aspect ratio and higher modes on the natural frequencies of NDNPS is studied in this manuscript. Present work may provide an analytical scale-based nonlocal approach which could serve as the starting point for further investigation of more complex n-nanoplates systems arising in future generation graphene based nanocomposites.