Dynamic Behavior Analysis For Several Typical Micro/nano Structures

With the deep understanding of the nature and the continuous development of science and technology,the perspective of human has gradually shifted from the macroworld to the microworld.Due to excellent performance,micro/nano materials and structures has attracted great attentions of scientists.With the further development of micro/nano manufacturing technology,clarification of the mechanical responses of micro/nano materials and structures under different external fields has become more and more urgent.In this dessertation,aiming to the cell membrane,the most important microstructure in the nature,as well as carbon nanotube and graphene,the most typical and artificial nanomaterials,cell membrane morphological evolution and its stability,as well as wave propagation in viscoelastic graphene sheets and carbon nanotubes,are discussed.The main contents are as follows:1.The shape equation of vesicles under an alternating electric field is established based on the electromechanical liquid crystal model.The effects of frequency,osmotic pressure and surface tension on the morphological evolution of vesicles are discussed.The relationships between osmotic pressure,surface tension and morphology of vesicle are clarified.At the same time,the singularity of the alternating electric field for biconcave vesicles is analyzed.The frequency-dependent singularity of the alternating electric field is clarified.In addition,the morphological stability of cell membranes with cross-linking protein structures under a direct current electric field is investigated.The critical electric field strength of cell membranes is obtained by deriving the second variation of free energy.The effects of cell radius,permittivity difference of inner and outer media,stiffness of cross-linking protein structures and osmotic pressure on the critical electric field strength of cell membrane are discussed.The relationships between cell radius,permittivity difference of inner and outer media,stiffness of cross-linking protein structures,osmotic pressure and morphological stability criterion of cell membranes are clarified.2.Viscoelastic stress wave propagation in viscoelastic single-and double-walled carbon nanotubes is studied based on the nonlocal strain gradient Timoshenko beam model.The effects of material and structural parameters on the propagation characteristics of stress waves are discussed.It is found that there exsit critical diameters for stress waves in the viscoelastic carbon nanotubes due to viscosity and size effect of carbon nanotubes.The influences of viscous damping coefficient,size effect and Van der Waals force have significant effects on the critical diameters for stress waves.In addition,viscoelastic wave propagation in viscoelastic single-layer graphene sheets is investigated based on the nonlocal gradient Mindlin plate model.The influences of viscous damping coefficient,size effect,magnetic field and elastic foundation on the propagation characteristics of extensional waves,flexural wave and shear waves in the viscoelastic single-layer graphene sheets are discussed.The cut-off wave numbers for extensional waves,flexural wave and shear waves are observed.The influences of viscous damping coefficient,size effect and magnetic field on the cut-off wave numbers are clarified.3.The governing equations for forced vibration of temperature-dependent functionally graded nanobeams are derived based on the nonlocal strain gradient Euler-Bernoulli beam model and physical neutral surface.The material parameters of functionally graded nanobeams change continuously along the thickness direction according to the power-law function or sigmoid function.Closed-form approximate solution for nonlinear forced vibration is obtained by using multiple time scale method.The influences of neutral surface deviation caused by temperature variation and gradient index,nonlinear elastic foundation and size effect on the nonlinear resonance of the FG nanobeams are discussed.The numerical results show that if the in-coincidence of physical and geometrical neutral surfaces is ignored,the hardening-type behavior of the systems will be underestimated.The influences of temperature variation,size effect,and stiffness of nonlinear elastic foundation on the underestimation of the hardening-type behavior are clarified.