Theoretical Study On Nonlocal 2D Nano-mechanics And Preliminary Exploration For Dynamics Of A Bouncing Ball-sheet System

Being three forefronts of high-tech in 21 st century, information, biotechnology and nanotechnology are advancing social development and changing the human life rapidly. The rapid development of nanotechnology enables the precise manufacture of nanoscale units and corresponding application in NEMS structure. Currently, the NEMS has penetrated into all fields of human life and science and technology development, including macro to micro, medical technology to the life science, manufacturing to information communication, etc. As one of basic NEMS structure, nanosheet is also basic mechanics model of the twodimensional graphene. Controlling the mechanical properties of nanosheet is the indispensable prerequisite for process of design, optimization and packaging in NEMS. Therefore, in-depth study of the mechanical properties of nanosheet has an important theoretical significance and engineering application value.A large number of experimental results confirmed that the nanostructures have some mechanical effects differences with theory prediction in macro-scale, so classical mechanics has not been directly used in nanostructures. At present, the research of mechanical behavior of nanostructures includes experimental research, molecular dynamics simulations and improved continuum mechanics, wherein the nonlocal theory proposed by Eringen has wide range of application in nano-mechanics.However, there exist two contrary types of elastic models in nonlocal field theory. The two contradictory predictions cannot be unified, which hindered further development and application of the theory. Therefore, firstly this article will focus the study on nonlocal theory itself to perfect the theories and unify models. Secondly, statics and dynamics models of nanosheet have been established based upon nonlocal theory and Kirchhoff plate theory to have corresponding mechanical properties analyzed. Particularly, size-dependent for forced vibration response of nanosheet under pulse load has been studied, and preliminary exploration of dynamic experiment of a bouncing ball-sheet has been conducted. Details are as follows:For two types of opposite nonlocal elastic model, taking nanobeam as an example, the pinned-pinned, cantilever, clamped at both ends of the beams under different boundary conditions and loadings are analyzed, and effects of nonlocal scale factor on the bending stiffness is determined. By employing an iteration method, expression of nonlocal high-order stress is achieved based on the gradient type of nonlocal differential constitutive model, then the control equation of nonlocal high-order gradient type beam model is obtained. The nonlocal deflection is solved via the regular perturbation method. The results show that: Within gradient type nonlocal differential constitutive framework, the stiffness of nanostructures may be reduced or enhanced or the same as classical structures, and the trend depends on external loads and boundary constraints.Research of the static deflection and lateral free vibration response of nanosheet has been conducted based upon stiffness weaken model in nonlocal elasticity theory. Nonlocal stress expression has been obtained with iteration method, and control equation of nanosheet has been established. Analytical solution of static deflection and natural frequency of the nanosheet with simple support has been obtained to reveal the effects of small-scale coefficient, number of half-wave and three-dimensional sizes on static deflection and frequency responses of the nanosheet. Results show that with the increase of small-scale parameters, the static deflection increases, the equivalent stiffness and natural frequency is reduced. Static deflection and natural frequency increases as the number of half-wave increases, and decreases with the increase of nanosheet length and width. The natural frequency increases as thickness increases.The displacement of nanosheet with simple support under dynamic loads has been solved with Navier method. The effects of small-scale parameter, number of half-wave and three-dimensional sizes of nanosheet on the forced vibration have been discussed. The results show that displacement and amplitude have significant nonlocal effect under uniform load, however, they are not shown in pulse dynamic load. Under uniform dynamic load, forced amplitude increases with the increase of small-scale parameters, number of half-wave and length and width, decreases as the thickness increases.Experiment platform for research of dynamics of a bouncing ball-sheet has been designed and built up. Through extracting and processing the acoustic emission signal of impact between ball and sheet, the influences of vibration frequency, amplitude and the ball mass on collision interval and strength have been analyzed. It is concluded that both ballsheet collision interval and the impact strength does not have fixed values, but a state of distribution has been presented in a certain range. Ball-sheet collision interval and impact strength increases with the increase of frequency and amplitude, decreases with the increasing ball mass.Being normal nanosheet components in NEMS, the comprehensive mechanical properties of two-dimensional nanosheet, particularly scale-dependent properties, have been revealed in this study. The nonlocal elastic theory model has been improved which will provide useful supplement and expand to the development of solid mechanics, meanwhile it will provide a theoretical basis for the performance prediction and optimization design of new nanoscale devices.