| Graphene is a new type of nano-material after the discovery of the carbon nanotubes.The graphene material has a hexagonal honeycomb crystal lattice structure,has excellent mechanical,thermal and electrical properties,and is a research material in the front of the world,and has wide application prospect.In this paper,taking the aircraft wing as the background,considering the mechanical properties of graphene reinforced composites,the aircraft wing is simplified as a cantilever plate model,and the nonlinear dynamic characteristics of graphene reinforced composite plate structure are studied.The nonlinear kinematic equations of laminated plates are established,the natural frequencies of different laying forms of laminated structures are calculated,and the nonlinear vibration and 1:1 internal resonance response of laminated structures with external excitation are analyzed.The main content of this paper is divided into the following aspects:(1)The equivalent Young’s modulus of graphene composites was calculated by Halpin-Tsai uniform mixing model,and the Poisson’s ratio and density of graphene composites were calculated by mixing rate.The dynamic model of composite laminates is established.Based on the first-order shear deformation theory,von Karman deformation theory,the nonlinear dynamic equation of laminated plates under transverse load is established by using Hamilton principle.The combined modal function of cantilever beam and free beam is selected and discretized by Galerkin method to obtain the nonlinear ordinary differential equation of graphene composite laminates.(2)The vibration amplitude of the structure under the lateral excitation is studied by the numerical simulation method,and the influence of the non-linear factors on the vibration response of the structure is analyzed.In this paper,the dynamic response of the cantilever structure under the same excitation is obtained in the case of linear system,nonlinear term and non-linear term.It is found that the non-linear term has an obvious influence on the vibration stability of the structure,and the vibration response characteristics of the structure have some similarity under different nonlinear terms.The influence of the non-linear term change of a first order natural frequency on the structure vibration response is also investigated.The results show that the non-linear term change of the first order natural frequency causes the phase trace line of the structure to exhibit wave characteristics,and the non-linear term changes at the second order natural frequency,so that the phase trace line of the structure exhibits self-expandingproperty.(3)By optimizing the basic function,the potential energy of boundary conditions is established,and the natural frequency of cantilever laminated plates is solved by Rayleigh-Ritz method.The natural frequency and vibration mode calculated by Rayleigh-Ritz method are compared with the finite element program,and the results are in good agreement with each other.At the same time,the effects of graphene content,thickness of laminated plates and aspect ratio on the natural frequency of the structure were analyzed.(4)In the above analysis,it is found that the second and third natural frequencies of laminated plates have the characteristic of 1:1.Combined with the characteristics of nonlinear vibration,the nonlinear dynamic characteristics of graphene composite laminated plates under the internal resonance of 1:1 are analyzed.The frequency response curves of the system in polar and rectangular coordinates are studied,and the results show that the structure shows the characteristics of hard spring.The influence of external excitation and damping coefficient on the vibration response of the structure is discussed.It is found that with the increase of damping coefficient,the motion characteristics of the structure are gradually stable.With the increase of external excitation,the motion characteristics of the structure appear alternately between periodic and chaotic motion. |
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