Surface Effect On The Mechanical Properties Of Nanowires And Nanoplates

The past decade has witnessed the successful development of nanostructures such as ultrathin nanoplates (nanofilms), nanowires, and nanotubes, all of which have novel and remarkable physical properties. Nanowires and nanoplates are one of the most important basic elements of nanoelectromechanical systems owing to their wide application as devices such as sensors, resonators, transistors, and actuators. Thus, a surge of interests has been attracted in research communities for the physical properties and mechanical characters of nanowires and naoplates. There are fewer bonding neighbors of surface atoms for nanostructures which distinguishes them from their macroscopic bulk counterparts. As nanostructures shrinks to several nanometers, the broken bond at surface relaxes and the charge redistributes. The nanostructures usually carry lowered symmetry corresponding to bulk counterpart and need additional elastic, magnetoelastic and electroelastic constants because of the small thickness. Due to the large ratio of surface area to volume typically presented in nanomaterials, the surface effects could not be omitted. But the popular models taking the effect of surface elasticity into consideration are either completely idea or lead to an unrealistic physical image.This thesis is focuses on the constitutive equation and Young’s modulus for different axial-oriented nanowires and naoplates, the surface elastic theory for describing the buckling and vibration of nanowires based on the Euler-Bernoulli beam (EBB) and Timoshenko beam (TB) theory and the surface effect on the bending and vibration of nanoplates by considering surface effects, symmetry lowering and additional elastic constants.Firstly, we obtain the constitutive equation and Young’s modulus for<100>, <110> and<111> axial-oriented nanowires and nanoplates. We also have an important conclusion that there is the orthorhombic anisotropy in<110> axial-oriented naoplates and monocline anisotropy in<111> axial-oriented naoplates.Secondly, we describe the axial buckling and vibration of nanowires by structural models that include symmetry lowering, surface effects and additional elastic constants in the framework of Euler-Bernoulli beam theory. We have examined the validity and the applicability of our model by comparing the theoretical solutions with relevant experimental results as well as numerical computational results and core surface model.Thirdly, the Timoshenko beam theory integrated with surface effects is employed to derive the analytical solutions of the critical buckling force and the natural vibration frequency. We have examine the coupled effects of surface elasticity, residual surface stress, transverse shear deformation and rotary inertia on the axial buckling and transverse vibration behaviour of nanowires by comparing with our theory based on Euler-Bernoulli beam model, core-surface model with Euler-Bernoulli beam theory and Timoshenko beam theory, the simulated results of density of function theory (DFT) and molecular dynamics (MD) theory.Finally, an analytical method is presented to study the size dependent bending behavior under uniformly distributed load and free vibration of rectangular nanoplates using a generalized form of Kirchhoff plate model by considering surface elasticity, residual surface stress and symmetry lowering. It is shown that the surface effects are more prominent in thinner plates and those with higher aspect ratios alb and lower aspect ratios alh for bending and vibration characteristics.