Small Scale Effects In Micro-/Nano-Structures

With the rapid development of nanotechnology,micro-/nano-structures have been widely used in design and fabrication of micro-/nano-electromechanical systems.For better designing and utilizing these microscale and nanoscale structures,it is of great importance to study their mechanical behaviors.It has been shown that mechanical behaviors of structures in small scale are quite different from those in macroscale,exhibiting remarkable size-dependency,namely size effects.Nonlocal effect,strain gradient effect and surface effect are three typical types of size effects in micro-/nano-scale.In this work,based on the continuum mechanics modelling approach,a theoretical framework which can simultaneously incorporate nonlocal effect,strain gradient effect and surface effect is constructed,the influences of these typical types of size effects on the mechanical behaviors of small-scaled beams,plates and shells,which are basic building blocks of micro-/nano-electromechanical system,are investigated.Moreover,negative mass effects in graphene and carbon nanotube are discovered,and dynamic behaviors of graphene-based and carbon nanotube-based micro-/nano-scale elastic metamaterials are studied.The main contributions of the present work are listed below:1)Based on the nonlocal strain gradient theory,a unified beam model which incorporates nonlocal effect and strain gradient effect simultaneously is developed.By choosing appropriate shape functions,the proposed model can be degenerated to Euler-Bernoulli beam model,Timoshenko beam model as well as various higher-order beam models.Through the Navier series method,analytical solutions for natural frequencies,deflections and critical buckling loads of simply supported nanobeams are obtained.Then,the influences of nonlocal effect and strain gradient effect on the vibration,bending and buckling behaviors of nanobeams are investigated.2)By using the nonlocal strain gradient theory and the surface elasticity theory,a unified plate model which captures nonlocal effect,strain gradient effect and surface effect simultaneously is established.By choosing appropriate shape functions,the proposed model can be reduced to Kirchhoff plate model,Mindlin plate model as well as various higher-order plate models.Through the assuming modal function method,analytical solutions for critical buckling loads of rectangular nanoplates with various boundary conditions are acquired.Then,the influences of nonlocal effect,strain gradient effect and surface effect on the buckling behavior of nanoplates are analyzed.3)With the help of the nonlocal strain gradient theory and the surface elasticity theory,a size-dependent functionally graded shell model which incorporates nonlocal effect,strain gradient effect and surface effect simultaneously is derived.Through the assuming modal function method,analytical solutions for natural frequencies of functionally graded cylindrical nanoshells under different boundary conditions are obtained.Then,the influences of nonlocal effect,strain gradient effect and surface effect on the vibration characteristic of functionally graded cylindrical nanoshells are examined.4)A continuum mechanics model for vibration analysis of multilayer graphene sheets under layerwise tension forces is developed.From the analysis of the resonance between the inner layers and the outer layers,it is shown that a multilayer graphene sheet with highly tensioned outerlayers but tension-free inner layers can exhibit negative effective mass density with a certain frequency range like elastic metamaterials.Based on this finding,the dynamic behavior of graphene-based micro-/nano-scale elastic metamaterial is investigated.5)A continuum mechanics model for dynamical analysis of carbon nanotubes filled with a mass chain is established.From the study of the resonance between the inserted mass chain and the carbon nanotubes,it is found that a filled carbon nanotube can exhibit negative effective mass density with a certain frequency range like elastic metamaterials.On the basis of this finding,the dynamic behavior of carbon nanotube-based micro-/nano-scale elastic metamaterial is analyzed.