Nonlinear Static And Dynamic Analysis Of Piezoelectric Nanowires Considering Surface Energies

Nanowires have many technologically important applications as, for instance, sensors, actuators, transistors and resonators in nano-electromechanical systems (NEMS), biotechnology, electronics, and photonics. Due to the increasing ratio of surface area to volume, the physical and mechanical properties of nanowires often exhibit distinct size dependence. In this dissertation, considering piezoelectric nanowires under electric field conditions as the subjects investigated, taking into account the impact of geometric nonlinearity, piezoelectric effects, surface energies and other factors, the static and dynamic behaviors of the piezoelectric nanowire are studied, which reveals the essential characteristics of the mechanical behaviors of the structures. The main research works are as follows.First of all, nonlinear static mechanical behavior of the piezoelectric nanowires under the electrical excitation are investigated. Based on continuum mechanics theory and Euler-Bernoulli hypothesis, when a direct current(DA) voltage is applied, the nonlinear governing equations of piezoelectric nanowires considering surface effects are established. The Galerkin is used to solve the governing equations. Numerical examples are examed for a nanowire supported between axiallay immobile surpports. The results give the influence of the size effects and surface energies on the buckling load and the post-buckling path. Then, the nonlinear free vibrations of the piezoelectric nanowires are studied by utilizing multiple-scale method. The influence of size effects and applied voltages on the nonlinear free vibration frequency and amplitude-frequency response curve are discussed.Furthermore, the dynamic stability of a piezoelectric nanowire is studied using the Floquent theory. When an alternating current (AC) voltage is applied to the nanowire, based on Euler-Bernoulli beam theory, the partial differential governing equation is inverted into an ordinary differential equation by utilizing Galerkin method. Then the incremental harmonic balanced method is applied to get the corresponding numerical solutions. In the numerical examples, the effects of the surface energies, AC voltage amplitude and geometric nonlinearity on the principal region of instability are discussed.Finally, based on the continuum mechanics and the Timoshenko theory, the wave propagation properties of the piezoelectric nanowire are studied. Considering the surface energy and piezoelectric effect, the transverse vibration governing equations of a nanowire considering traverse shearing are derived. From the eigenvalue problem, the relationship between wave frequency(wave velocity) and control voltage are gotten. The influence of surface energy and piezoelectric effect on the motion of flexural wave and shear wave are dissussed.