Abstract
• Mathematical modeling of the nonlinear vibration behavior of graphene sheets is examined. • The element-free kp-Ritz method is employed to perform the numerical simulation. • Nonlocal elasticity theory is incorporated to account for the small scale effect. Due to their valuable and unique properties, graphene sheets (GSs) have attracted increasing attention in recent years. This paper presents the mathematical modeling of the nonlinear vibration behavior of GSs using classic plate theory and nonlocal elasticity theory which accounts for the size effect. The numerical solutions are obtained through the element-free kp-Ritz method. The iteration process is dealt with using the linearized updated mode method. The transformation method is used to impose the boundary conditions. The published results are used to verify the correctness of the present nonlocal element-free kp-Ritz method. The effects of boundary conditions, side length, aspect ratio and nonlocal parameters on the frequency–amplitude response are examined.
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