Nonlinear Dynamics Analysis Of Micro/Nano-beam Considering Damage

With the rapid development of modern machinery, micro/nano electro mechanical has been widely used. In the early 21 stcentury, MEMS and NEMS are widely applied into all kinds of micro devices. The small size of the MEMS and NEMS enables them to exhibit different mechanical properties, such as surface effect, size effect and tunnel effect, etc.Moreover, in practice, it is inevitable for the micro devices to get damaged in the process of manufacturing and usage. Hence, based on the above problems, the present dissertation has carried out the following studies:Firstly, on the basis of Euler-Bernoulli beam theory and Hamilton principle, the nonlinear governing equations of the nano-beam are derived. In addition, the Galerkin method and the Harmonic Balance Method are adopted to give a solution to the equation. By adopting numerical analysis method, the effects of nano-beam length, nano-beam thickness,damage factor and surface effect to curves of amplitude-frequency response of the nano-beam are discussed.Secondly, based on Gurtin-Murdoch theory and Hamilton principle, the nonlinear governing equations of the nano-beam are derived. In addition, the Galerkin method and Runge-Kutta method are adopted to give a solution to the equation. The critical condition of pull-in instability is investigated and the influence of material parameters and system parameters on critical condition is analyzed.Finally, the micro/nano-beam model is established on the basis of Euler-Bernoulli beam theory. And the mixed electrical load is antiphased, and moreover, the dynamic characteristics of the micro/nano beam are analyzed. In addition, the Duffing equation is derived from the Hamilton principle, and the Galerkin method and Runge-Kutta method are adopted to obtain solutions to the equation. The bifurcation and chaos under damping parameter, piezoelectric voltage and damage parameter are also discussed in detail.