**Mohammad Sadegh Nematollahi 1, Hossein Mohammadi 1,\*, Rossana Dimitri <sup>2</sup> and Francesco Tornabene 2,\***


Received: 18 July 2020; Accepted: 14 August 2020; Published: 15 August 2020

**Abstract:** We provide an analytical investigation of the nonlinear vibration behavior of thick sandwich nanocomposite beams reinforced by functionally graded (FG) graphene nanoplatelet (GPL) sheets, with a power-law-based distribution throughout the thickness. We assume the total amount of the reinforcement phase to remain constant in the beam, while defining a relationship between the GPL maximum weight fraction, the power-law parameter, and the thickness of the face sheets. The shear and rotation effects are here considered using a higher-order laminated beam model. The nonlinear partial differential equations (PDEs) of motion are derived from the Von Kármán strain-displacement relationships, here solved by applying an expansion of free vibration modes. The numerical results demonstrate the key role of the amplitudes on the vibration response of GPL-reinforced sandwich beams, whose nonlinear oscillation behavior is very important in the physical science, mechanical structures and other mathematical analyses. The sensitivity of the response to the total amount of GPLs is explored herein, along with the possible effects related to the power-law parameter, the structural geometry, and the environmental conditions. The results indicate that changing the nanofiller distribution patterns with the proposed model can remarkably increase or decrease the effective stiffness of laminated composite beams.

**Keywords:** functional reinforcement; graphene nanoplatelets; higher-order shear deformable laminated beams; nanocomposites; nonlinear free vibration; sandwich beams
