Nonlinear Dynamic Analysis Of Graphene Composite Plates And Shells Under Different Scales

Due to its good conductivity,high specific strength and excellent thermal conductivity,graphene(GP)has aroused great waves in the scientific community,providing a new opportunity for human beings to develop high-performance structural products.In the past " the 13 th Five-Year Plan",the state has deepened the policy shift to supply more investment in graphene and other new materials,which shows that the development of graphene and its derivatives is an important research direction in the field of composite materials.In this paper,a new three-phase composite structure(MFC-GP)is proposed based on the research background of the wing skin and the radiator of microelectronics.The complex nonlinear dynamic behavior of this kind of structure is studied under different working conditions,and the influence of different parameters on the dynamic characteristics of the structure is analyzed.This not only provides a new idea for the field of aircraft structure design,but also provides a new applicable material and theoretical guidance for solving the heat dissipation problem of microelectronic devices.The research content of this paper is mainly divided into the following parts:(1)Firstly,on the macro scale,based on the first-order shear deformation theory,Von Kármán geometric nonlinear relation,Hamilton principle and Galerkin discrete method,the mechanical-electrical coupling equations of MFC-GP cantilever plate are derived under transverse load and external voltage.The influence of graphene volume fraction and external voltage on the linear frequency of the structure are analyzed by eigenvalue method,and compared with the finite element method.Then,the frequency response equations of the structure are obtained under 1:2 internal resonance by multi-scale method.The influence of graphene volume fraction,piezoelectric coefficient and external excitation amplitude on the frequency response curve are analyzed and the influence of different parameters on the dynamic stability of MFC-GP cantilever plate structure are discussed.(2)The influence of thermal effect on the dynamic characteristics of MFC-GP simply supported plate structure is investigated.Using the modeling method in Chapter 2,the mechanical-electrical-thermal coupling equations of MFC-GP simple support plate are derived under transverse load,external voltage and temperature field.The linear frequency of the structure are calculated under different graphene volume fraction and wave number by eigenvalue method.Then,the frequency response equations of the structure are obtained under 1:2 internal resonance by perturbation analysis and the influence of graphene volume fraction,voltage,temperature and external excitation amplitude on the frequency response curve are discussed under different coupling modes,and the nonlinear dynamic behavior of the structure is analyzed under specific parameters.(3)The nonlinear dynamic model of MFC-GP simple supported shell structure is established.Considering the large geometric deformation of the structure and based on the improved first-order shear deformation shell theory,energy principle and Galerkin discrete method,the mechanical-electrical-thermal coupling equations of MFC-GP simple supported shell are derived under the action of transverse load,external voltage and temperature field.The nonlinear dynamic behavior of the structure is analyzed under certain parameters by numerical simulation,and compared with the simply supported plate.(4)At the micro scale,the constitutive equation of MFC-GP is established based on Eringen's nonlocal elasticity theory.The governing equations of the nonlinear motion of the microplate are derived by using the classical plate theory,Von Kármán geometric nonlinearity and Hamilton principle.Then,by using Green-Naghdi generalized non-dissipative thermo elastic coupling theory and Galerkin's weighted residual method,the thermo-elastic coupling equations of MFC-GP simple supported microsheet are established under non-uniform thermal field.Considering the positive piezoelectric effect of graphene and piezoelectric fiber,the coupling equation of electric field is given.Finally,the coupled mechanical-electrical-thermal equations of MFC-GP are obtained by Galerkin method.(5)Based on the global residual harmonic balance method,the first-order nonlinear frequency expression of MFC-GP is obtained.The influences of graphene volume fraction,nonlocal parameters,aspect ratio,damping coefficient and order parameters on the nonlinear frequency of the structure are discussed.The frequency response equations of the structure are obtained under the main resonance by the perturbation method and the influence of graphene volume fraction,nonlocal parameters,aspect ratio and external excitation amplitude on the frequency response curve of the structure are analyzed.Based on the motion coupling control equations of the structure,the influence of different parameters on the dynamic stability of MFC-GP simply supported microsheet is discussed.