Dynamic Response of Functionally Graded Epoxy/Graphene Nanoplatelet Composite Lattice Nanostructures

The primary objective of this study is to investigate the vibrational behavior of functionally graded (FG) lattice nanostructures composed of epoxy reinforced with graphene nanoplatelets (GPLs) by devel- oping a novel finite element method (FEM) within the framework of nonlocal strain gradient elasticity theory. The governing equations are formulated based on Euler–Bernoulli beam theory, assuming that the effective material properties vary continuously through the beam thickness according to a power- law distribution. To account for size-dependent effects, the classical formulation is enhanced using the strain gradient nonlocal elasticity model, enabling accurate representation of coupled axial and bend- ing responses at the nanoscale. The finite element formulation is derived from the weak form of the strain gradient differential problem which accounts also for dynamic effects. By introducing additional degrees of freedom (DOF), Higher-order Hermite interpolation functions are employed to satisfy the re- quired continuity conditions for both axial and bending kinematics, leading to a multi-degree-of-freedom frame element capable of capturing axial–bending coupling due to material inhomogeneity. Numerical validation demonstrates excellent agreement with available analytical results under various boundary conditions. Furthermore, comparative analyses highlight the advantages of the proposed formulation over classical finite element approaches and analytical solutions. The influence of nonlocal parameters and geometric characteristics on the natural frequencies of straight and curved FG lattice nanostruc- tures is systematically examined, demonstrating the efficiency and accuracy of the proposed method for nanoscale structural analysis and NEMS applications.