This study investigates the size-dependent free vibration analysis of multi-layered graphene sheets based on exponential shear deformation theory (ESDT), which considers the effects of rotary inertia and transverse shear deformations. In order to capture the effects of length scale parameter on the vibrational behavior of the structure, modified strain gradient elasticity theory is utilized. An elastic multiple-plate model is assumed in which the nested plates are coupled with each other through the van der Waals interlayer forces. The governing equations of motion are derived by implementing Hamilton’s principle and then are solved with the Navier approach. To verify the present model, results in specific cases are compared with the available papers in the literature and excellent agreement is seen. Finally, the effects of various parameters such as aspect ratio, thickness ratio, Winkler modulus, shear modulus, and size effects on the natural frequencies of a multi-layered graphene sheet are presented and discussed in detail.
