Mechanical Properties Of One-dimensional Nanostructures And Piezoelectric Nanostructures Based On Non-classical Continuum Theories

Nanomaterials and structures have excellent physical,chemical,mechanical and electrical properties,as well as great potential and application in many frontier areas of science and technology.In science,the integration of nano-scale and classical mechanics has resulted in the interdisciplinary study of nano-mechanics.In technology,micron scale and even nano scale structural units can be accurately manufactured which is applied to nano-electro-mechanical systems(NEMS)by modern science and technology.As the basic component of the nano-systems,especially for NEMS,one-dimensional nano-beams should be studied systematically.Nano-beams bear the influence of complex internal and external environmental in the system or other devices.Therefore,based on the effective micro-theory research and the control of various mechanical properties of nano-beams,it will provide a theoretical basis for the micro-design,assembly and regulation of one-dimensional nanostructures.At present,a large number of theoretical and experimental studies have proved that the scale effect is significant when the microstructures at nanoscale which cannot be ignored.In this paper,one-dimensional nanostructures are the research object,studied by non-local theory and non-local strain gradient theory.The scale effect is the core research object.The governing equations and boundary conditions of nano-beams under different model backgrounds are established.The governing equations of the models are solved by effective analysis or numerical methods,after that,the bending moment,the deflection,the vibration frequency and the stability of the nano-beams with small-scale parameters are discussed.The specific contents are as follows:(1)Based on Eringen’s non-local theory,the bending of the flexible nanorods subjected to multiple axial and transverse loads is studied.The equilibrium equation is derived and its non-local analytical solution is obtained.The numerical examples show that the non-local effect and bending stiffness are coupled which has a significant effect on the bending deformation of the flexible nanorods.The increase of axial and transverse loads will lead to the increase of bending deflection with a significant scale effect,that is,the basic mechanical variables change with the non-local scale parameters.From the relationship between bending stiffness and deflection or bending moment,it is deduced that there is a critical threshold for the bending stiffness of a particular model.When the bending stiffness of the material is less than the critical value,the nanorods will lose stability.(2)Based on the research above,the dynamic impact behavior of the nanostructures is studied.By non-local theory,the dynamic behavior of nano-components or nano-electronic components under impact is studied by simulating nano-components or nano-electronic components with cantilever nano-beams.The important physical quantities such as the non-local bending moment,the non-local deflection and the non-local dynamic load coefficient are deduced theoretically.The maximum non-local impact stress,the maximum non-local deflection and the non-local dynamic load coefficients were calculated to investigate the effects of the non-local small-scale parameters on the impact performance of the nano-cantilever beams.The results show that the existence of non-local effect effectively reduces the non-local impact stress,and then reduces the non-local deflection and the dynamic load coefficient.(3)Based on the research above which is one-dimensional nanostructures based on non-local theory,the theoretical method and research object are changed to study one-dimensional piezoelectric nanostructures by non-local strain gradient theory.Considering that the non-local strain gradient theory is more suitable for nano-mechanics,especially for the mechanical-thermal-electrical multi-field coupling dynamic behavior,the vibration characteristics and stability analysis of piezoelectric nano-beams under multi-field coupling are studied by the non-local strain gradient theory proposed by Lim et al.in 2015.Based on the non-local strain gradient theory,a multi-field coupled dynamic model is derived,and the governing equation is solved numerically by differential quadrature method(DQM).The numerical results show that the natural frequencies of piezoelectric nano-beams are weakened and strengthened by non-local small-scale parameters and strain gradient characteristic parameters respectively.These two effects are coupled and interdependent in the micro-structures,besides the interaction intensity is the same.The effects of thermal field,electric field and external force field on piezoelectric nano-beams are independent with the effects of non-local small-scale parameters and strain gradient characteristic parameters on piezoelectric nano-beams.There are critical values for each of them,and when they exceed the critical value,the system will be unstable.