Electro-induced nonlinear dynamic responses of graphene nanoplatelets-reinforced composite beams with size-dependent effects

A comprehensive understanding of the concurrent influence of dielectric properties and size-dependent effect on the dynamic behavior of graphene platelet-reinforced composite (GPLRC) beams is pivotal for their application in advanced intelligent composite structures. This study investigates the dynamic characteristics of GPLRC beams under an electric field, accounting for both dielectric and size-dependent effects. The graphene nanoplatelets (GPLs) are distributed through the beam thickness according to three distinct gradient patterns. The effective elastic modulus and dielectric permittivity of the composite are estimated using effective medium theory, whereas the effective Poisson's ratio and mass density are obtained via the linear rule of mixtures. Employing Timoshenko beam theory and nonlinear strain-displacement relationships, the governing equations for the dynamic behavior of the GPLRC beams are derived using the variational principle. These equations are then solved numerically by integrating the Rayleigh-Ritz method with the Runge-Kutta method, yielding the structure’s dynamic characteristics. A systematic analysis is conducted to elucidate the effects of DC voltage, initial axial stress, nonlocal parameter and average volume fraction of GPLs. Results indicate that increasing DC voltage enhances electrostatic stress, increasing peak midpoint deflection in beams with high GPLs content, while at low GPLs content deflection remains dominated by elastic stiffness. Conversely, higher initial axial stress enhances axial rigidity, thereby suppressing vibration. Additionally, increasing the average volume fraction of GPLs elevates the composite’s elastic modulus, resulting in a slight reduction in vibration amplitude.