Dynamic characteristics of multilayer graphene considering nonlinear higher-order strain gradient

This study adopts a higher-order simulation framework to investigate wave propagation in two-dimensionaldefect-freemultilayergraphene, incorporatinggeometricnonlinearitythrough second strain gradient elasticity. To accomplish this, the strong and weak forms governing π-bonds associated with van der Waals interactions and σ-bonds are derived using continuum beammodels. Thedynamicpropertiesofmultilayergraphene, includingbandstructures, slow- ness surfaces, and energy flow, are analyzed using the theory of periodic structures. Numerical results reveal that accounting for nonlinearity predicts higher frequency values, indicating a stiffness hardening effect in graphene. At high frequencies, energy is predominantly confined to a single direction, and the nonlinear model demonstrates a strong wave-controlling capa- bility compared to the linear model. This innovative study advances our understanding of graphene’s dynamic behavior and offers significant insights for engineering applications in- volving graphene-based nanocomposites.