Vibration Characteristics Of Graphene Nanobeams Based On Nonlocal Elasticity Theory

Nanoscale graphene nanoribbons will produce a certain small-scale effect.The resonance behavior and resonance law must be different from the macroscopic scale.The research methods are also different.Therefore,the research on the resonance characteristics of graphene nanobeams is The development and application of NEMS resonant sensors are of great significance.In this thesis,the nonlinear vibration characteristics of graphene nanobeams are studied based on non-local elastic theory method.The applicability of the theory is verified by molecular dynamics simulation method.The vibration characteristics of graphene nanobeams are extended from vacuum environment to medium environment.Resonant device design and engineering applications lay a foundation.The main research contents include:Firstly,a briefly introduction of NEMS devices and graphene properties were introduced.And the research progress of graphene resonance characteristics by different research methods at domestic and abroad at present were summarized.Secondly,based on the nonlocal elastic theory and the Euler-Bernoulli beam model,the nonlinear lateral free vibration model of the double-ended simply supported graphene nanobeams is analyzed.The differential equation of the lateral vibration of the nanobeam is obtained by the Hamiltonian principle.The analytical solution to the natural frequency of the vibration system is obtained by using He's variational method.Through the solution and analysis of numerical examples,the following conclusions are obtained,the natural frequency of graphene nanobeams decreases with its aspect ratio increases.the natural frequency has an increasing trend with increasing amplitude or increasing temperature.The nonlocal parameter have a significant effect on the natural frequency of graphene nanobeams.Thirdly,the basic principle and initial condition setting of molecular dynamics simulation method.The simulation environment,simulation software and simulation process of singlelayer graphene nanobeam are described.The modeling process of graphene nanobeams system is described in detail.Then,the molecular dynamics simulation was used to analyse the free vibration characteristics of graphene nanobeams.The results of relaxation properties and stress loading properties of graphene nanobeams were analyzed.Finally,The simulation of the free vibration natural frequency of graphene nanobeams under vacuum environment demonstrates that the applicability of nonlocal elastic theory in the nonlinear natural frequency of single-layer graphene nanobeams.Finally,the molecular dynamics simulations were carried out to incestigate the effects of gas damping on the damping vibration characteristics of graphene nanobeams.Comparing the result of the free vibrations,in the medium environment,the same uniform stress is applied,because of the existence of damping,the graphene nanoscale beam can be stabilized more quickly in the equilibrium position;Graphene nanobeams are more sensitive to less gas molecules,and the increase of environmental pressure will lead to the decrease of the natural frequency of graphene free vibration.When the environmental pressure increases to a certain extent,the effect of gas molecules on the nanobeams limited.In this thesis,the nonlinear resonance characteristics of graphene nanobeams are analyzed from two aspects of nonlocal elastic theory analysis method and molecular dynamics simulation calculation method,which provides a theoretical reference for the subsequent application of graphene nanobeams in resonant sensors.