Equivalent Modeling and Nonlinear Dynamics of Graphene Nanoplatelets Reinforced Regular Quadrilateral Truss Structures

PurposeEquivalent modeling and nonlinear dynamics of graphene nanoplatelets (GPLs) reinforced regular quadrilateral truss (RQT) structures are investigated.MethodsBased on energy equivalent principle and theory of Timoshenko beam, an equivalent beam (EB) of a rigidly connected GPLs reinforced RQT is developed. GPLs are distributed along the thickness direction or axial direction of each member of RQT. The elasticity matrix and inertial matrix of RQT periodic unit are deduced by means of both strain and kinetic energy equation. Rigidity matrix and mass matrix are derived from strain-displacement relationship. The frequencies and modes of RQT are obtained by eigenvalues and eigenvectors. On the basis of Von-Karman strain-displacement relation and Hamilton's Principle, the movement equation of nonlinear EB (NEB) with two simply supported edges are derived. Then we solve these equations with Galerkin and Runge-Kutta method.ResultsModal analysis of each order is performed. And the effects of GPLs distributions on the frequencies of RQT are also studied. The influence of external load, load frequency and system damping on the nonlinear dynamic behavior of NEB is analyzed.ConclusionsGPLs as a reinforcement can improve the frequency of RQT significantly. X distribution and V distribution along the thickness and axis directions respectively have the best enhancement effects. The influence of lateral damping on the nonlinear vibration response is greater than that of rotational damping. The amplitude and mode of nonlinear vibration are related to the load and frequency of external excitation.