Research On Mechanical Properties Of Functionally Graded Graphene Reinforced Composite Beams

Carbon matrix composites,which are based on carbon and reinforced by ceramic fibers such as carbon fiber or silicon carbide,play an increasingly important role for their advantages compared to traditional materials,such as light weight,high strength and good fatigue resistance.In this paper,functionally graded graphene reinforced composite beams are studied.The nonlinear longitudinal and transverse coupled vibration models of functionally graded graphene reinforced composite beams under transverse harmonic excitation in a thermomagnetic environment are established based on Hamilton's principle,Timoshenko beam theory and von Karman's geometric nonlinear theory.We use the Halpin Tsai model to calculate the equivalent Young's modulus,Poisson's ratio and density.We divided into linear and nonlinear models for solution analysis.In the linear part,the nonlinear term in the control equations are ignored.The nonlinear equations are transformed into linear differential equations.Then,the differential quadrature method is used to discretize it,so that the problem is transformed into solving linear equations.Furthermore,the problem of solving linear buckling load and free vibration frequency is transformed into the problem of solving eigenvalue of matrix.The influences of four kinds of graphene distribution patterns,graphene mass fraction,magnetic flux and temperature variation on the critical buckling load and linear vibration frequency of the beam are discussed in detail.In the nonlinear part,we use the Galerkin expansion to discretize the complete nonlinear control equations,then combine the incremental harmonic balance method and the arc length method to predict and correct solution curve.The results show that the amplitude peak and corresponding frequency of primary,2 super-harmonic and 3 super-harmonic resonances increase with the increase of dimensionless damping coefficient.In contrast,the change of the amplitude peak and corresponding frequency is slightly complicated when slenderness ratio increase.The amplitude peak of transverse motion increase,but corresponding frequency decrease.The frequency at amplitude peak of longitudinal motion decrease.The amplitude peak and corresponding frequency of rotational motion both decrease.Finally,the fourth order Runge Kutta method is used to verify the solution curve.